Maths Expansions Exercise3-2

Expansions Exercise 3.2

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Q11 If x + y = 8 and xy = 3 ¾, find the values of (i) x - y
(ii) 3 (x² + y² )
(iii) 5 (x² + y² ) + 4 (x - y).

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Q12 If x² + y² = 34 and xy = 10 ½, find the value of 2 (x + y)² + (x - y)²

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Q13 If a - b = 3 and ab = 4, find a³ - b ³ .

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Q14 If 2a - 3b = 3 and ab = 2, find the value of 8a³ - 27b³ .

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Q15 If x + 1/x = 4, find the values of
(i) x² + 1/x²
(ii) x⁴ + 1/x⁴
(iii) x³ + 1/x³
(iv) x - 1/x.

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Q16 If x - 1/x = 5, find the value of ⁴4 + 1/x⁴ .

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Q17 If x - 1/x = √5, find the values of
(i) x² + 1/x²
(ii) x + 1/x
(iii) x³ + 1/x³

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Q18 If x + 1/x = 6, find
(i) x - 1/x
(ii) x² - 1/x²

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Q19 . If x + 1/x = 2, prove that x² + 1/x² = x³ + 1/x³ = x⁴ + 1/x⁴ .

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Q20 If x - 2/x = 3, find the value of x³ - 8/x³

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Q21 If a + 2b = 5, prove that a³ + 8b³ + 30ab = 125.

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Q22 If a + 1/a = p, prove that a³ + 1/a³ = p (p² - 3).

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Q23 If x² + 1/x² = 27, find the value of x - 1/x.

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Q24 If x² + 1/x² = 27, find the value of 3x³ + 5x - 3/x³ - 5/x.

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Q25 If x² + 1/25x² = 8 3/5, find x + 1/5x

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Q26 If x² + 1/4x² = 8, find x³ + 1/8x³ .

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Q27 If a²
- 3a + 1 = 0, find (i) a² + 1/a²
(ii) a³ + 1/a³ .

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Q28 If a = 1/ (a - 5), find
(i) a - 1/a
(ii) a + 1/a
(iii) a²
- 1/a² .

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Q29 If (x + 1/x)² = 3, find x³ + 1/x³ .

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Q30 If x = 5 - 2√6, find the value of √x + 1/√x.

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Q31 If a + b + c = 12 and ab + bc + ca = 22, find a2 + b2 + c2 .

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Q32 If a + b + c = 12 and a2 + b2 + c2 = 100, find ab + bc + ca.

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Q33 If a2 + b2 + c2 = 125 and ab + bc + ca = 50, find a + b + c.

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Q34 If a + b - c = 5 and a2 + b2 + c2 = 29, find the value of ab - bc - ca

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Q35 If a - b = 7 and a² + b² = 85, then find the value of a³ - b ³

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Q36 If the number x is 3 less than the number y and the sum of the squares of x and y is 29, find the product of x and y.

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Q37 If the sum and the product of two numbers are 8 and 15 respectively, find the sum of their cubes.

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Expansions Exercise 3.2

Please Select

Q1 If x - y = 8 and xy = 5, find x² + y²

Q2 If x + y = 10 and xy = 21, find 2 (x² + y² ).

Q3 If 2a + 3b = 7 and ab = 2, find 4a² + 9b²

Q4 If 3x - 4y = 16 and xy = 4, find the value of 9x² + 16y².

Q5 If x + y = 8 and x - y = 2, find the value of 2x² + 2y² .

Q6 If a² + b² = 13 and ab = 6, find
(i) a + b
(ii) a - b

Q8 If p - q = 9 and pq = 36, evaluate
(i) p + q
(ii) p² - q ² .

Q9 If x + y = 6 and x - y = 4, find
(i) x² + y²
(ii) xy

Q10 If x - 3 = 1/x, find the value of x² + 1/x² .

Q11 If x + y = 8 and xy = 3 ¾, find the values of (i) x - y
(ii) 3 (x² + y² )
(iii) 5 (x² + y² ) + 4 (x - y).

Q12 If x² + y² = 34 and xy = 10 ½, find the value of 2 (x + y)² + (x - y)²

Q13 If a - b = 3 and ab = 4, find a³ - b ³ .

Q14 If 2a - 3b = 3 and ab = 2, find the value of 8a³ - 27b³ .

Q15 If x + 1/x = 4, find the values of
(i) x² + 1/x²
(ii) x⁴ + 1/x⁴
(iii) x³ + 1/x³
(iv) x - 1/x.

Q16 If x - 1/x = 5, find the value of ⁴4 + 1/x⁴ .

Q17 If x - 1/x = √5, find the values of
(i) x² + 1/x²
(ii) x + 1/x
(iii) x³ + 1/x³

Q18 If x + 1/x = 6, find
(i) x - 1/x
(ii) x² - 1/x²

Q19 . If x + 1/x = 2, prove that x² + 1/x² = x³ + 1/x³ = x⁴ + 1/x⁴ .

Q20 If x - 2/x = 3, find the value of x³ - 8/x³

Q21 If a + 2b = 5, prove that a³ + 8b³ + 30ab = 125.

Q22 If a + 1/a = p, prove that a³ + 1/a³ = p (p² - 3).

Q23 If x² + 1/x² = 27, find the value of x - 1/x.

Q24 If x² + 1/x² = 27, find the value of 3x³ + 5x - 3/x³ - 5/x.

Q25 If x² + 1/25x² = 8 3/5, find x + 1/5x

Q26 If x² + 1/4x² = 8, find x³ + 1/8x³ .

Q27 If a²
- 3a + 1 = 0, find (i) a² + 1/a²
(ii) a³ + 1/a³ .

Q28 If a = 1/ (a - 5), find
(i) a - 1/a
(ii) a + 1/a
(iii) a²
- 1/a² .

Q29 If (x + 1/x)² = 3, find x³ + 1/x³ .

Q30 If x = 5 - 2√6, find the value of √x + 1/√x.

Q31 If a + b + c = 12 and ab + bc + ca = 22, find a2 + b2 + c2 .

Q32 If a + b + c = 12 and a2 + b2 + c2 = 100, find ab + bc + ca.

Q33 If a2 + b2 + c2 = 125 and ab + bc + ca = 50, find a + b + c.

Q34 If a + b - c = 5 and a2 + b2 + c2 = 29, find the value of ab - bc - ca

Q35 If a - b = 7 and a² + b² = 85, then find the value of a³ - b ³

Q36 If the number x is 3 less than the number y and the sum of the squares of x and y is 29, find the product of x and y.

Q37 If the sum and the product of two numbers are 8 and 15 respectively, find the sum of their cubes.

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Expansions Exercise 3.2

Please Select

Q1 If x - y = 8 and xy = 5, find x2 + y2

Q2 If x + y = 10 and xy = 21, find 2 (x2 + y2 ).

Q3 If 2a + 3b = 7 and ab = 2, find 4a2 + 9b2

Q4 If 3x - 4y = 16 and xy = 4, find the value of 9x2 + 16y2.

Q5 If x + y = 8 and x - y = 2, find the value of 2x2 + 2y2 .

Q6 If a2 + b2 = 13 and ab = 6, find (i) a + b (ii) a - b

Q8 If p - q = 9 and pq = 36, evaluate (i) p + q (ii) p2 - q 2 .

Q9 If x + y = 6 and x - y = 4, find (i) x2 + y2 (ii) xy

Q10 If x - 3 = 1/x, find the value of x2 + 1/x2 .

Q11 If x + y = 8 and xy = 3 ¾, find the values of (i) x - y (ii) 3 (x2 + y2 ) (iii) 5 (x2 + y2 ) + 4 (x - y).

Q12 If x2 + y2 = 34 and xy = 10 ½, find the value of 2 (x + y)2 + (x - y)2

Q13 If a - b = 3 and ab = 4, find a3 - b 3 .

Q14 If 2a - 3b = 3 and ab = 2, find the value of 8a3 - 27b3 .

Q15 If x + 1/x = 4, find the values of (i) x2 + 1/x2 (ii) x4 + 1/x4 (iii) x3 + 1/x3 (iv) x - 1/x.

Q16 If x - 1/x = 5, find the value of 44 + 1/x4 .

Q17 If x - 1/x = √5, find the values of (i) x2 + 1/x2 (ii) x + 1/x (iii) x3 + 1/x3

Q18 If x + 1/x = 6, find (i) x - 1/x (ii) x2 - 1/x2

Q19 . If x + 1/x = 2, prove that x2 + 1/x2 = x3 + 1/x3 = x4 + 1/x4 .

Q20 If x - 2/x = 3, find the value of x3 - 8/x3

Q21 If a + 2b = 5, prove that a3 + 8b3 + 30ab = 125.

Q22 If a + 1/a = p, prove that a3 + 1/a3 = p (p2 - 3).

Q23 If x2 + 1/x2 = 27, find the value of x - 1/x.

Q24 If x2 + 1/x2 = 27, find the value of 3x3 + 5x - 3/x3 - 5/x.

Q25 If x2 + 1/25x2 = 8 3/5, find x + 1/5x

Q26 If x2 + 1/4x2 = 8, find x3 + 1/8x3 .

Q27 If a2 - 3a + 1 = 0, find (i) a2 + 1/a2 (ii) a3 + 1/a3 .

Q28 If a = 1/ (a - 5), find (i) a - 1/a (ii) a + 1/a (iii) a2 - 1/a2 .

Q29 If (x + 1/x)2 = 3, find x3 + 1/x3 .

Q30 If x = 5 - 2√6, find the value of √x + 1/√x.

Q31 If a + b + c = 12 and ab + bc + ca = 22, find a2 + b2 + c2 .

Q32 If a + b + c = 12 and a2 + b2 + c2 = 100, find ab + bc + ca.

Q33 If a2 + b2 + c2 = 125 and ab + bc + ca = 50, find a + b + c.

Q34 If a + b - c = 5 and a2 + b2 + c2 = 29, find the value of ab - bc - ca

Q35 If a - b = 7 and a2 + b2 = 85, then find the value of a3 - b 3

Q36 If the number x is 3 less than the number y and the sum of the squares of x and y is 29, find the product of x and y.

Q37 If the sum and the product of two numbers are 8 and 15 respectively, find the sum of their cubes.

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Q1 If x - y = 8 and xy = 5, find x² + y²

Q2 If x + y = 10 and xy = 21, find 2 (x² + y² ).

Q3 If 2a + 3b = 7 and ab = 2, find 4a² + 9b²

Q4 If 3x - 4y = 16 and xy = 4, find the value of 9x² + 16y².

Q5 If x + y = 8 and x - y = 2, find the value of 2x² + 2y² .

Q6 If a² + b² = 13 and ab = 6, find
(i) a + b
(ii) a - b

Q8 If p - q = 9 and pq = 36, evaluate
(i) p + q
(ii) p² - q ² .

Q9 If x + y = 6 and x - y = 4, find
(i) x² + y²
(ii) xy

Q10 If x - 3 = 1/x, find the value of x² + 1/x² .

Q11 If x + y = 8 and xy = 3 ¾, find the values of (i) x - y
(ii) 3 (x² + y² )
(iii) 5 (x² + y² ) + 4 (x - y).

Q12 If x² + y² = 34 and xy = 10 ½, find the value of 2 (x + y)² + (x - y)²

Q13 If a - b = 3 and ab = 4, find a³ - b ³ .

Q14 If 2a - 3b = 3 and ab = 2, find the value of 8a³ - 27b³ .

Q15 If x + 1/x = 4, find the values of
(i) x² + 1/x²
(ii) x⁴ + 1/x⁴
(iii) x³ + 1/x³
(iv) x - 1/x.

Q16 If x - 1/x = 5, find the value of ⁴4 + 1/x⁴ .

Q17 If x - 1/x = √5, find the values of
(i) x² + 1/x²
(ii) x + 1/x
(iii) x³ + 1/x³

Q18 If x + 1/x = 6, find
(i) x - 1/x
(ii) x² - 1/x²

Q19 . If x + 1/x = 2, prove that x² + 1/x² = x³ + 1/x³ = x⁴ + 1/x⁴ .

Q20 If x - 2/x = 3, find the value of x³ - 8/x³

Q21 If a + 2b = 5, prove that a³ + 8b³ + 30ab = 125.

Q22 If a + 1/a = p, prove that a³ + 1/a³ = p (p² - 3).

Q23 If x² + 1/x² = 27, find the value of x - 1/x.

Q24 If x² + 1/x² = 27, find the value of 3x³ + 5x - 3/x³ - 5/x.

Q25 If x² + 1/25x² = 8 3/5, find x + 1/5x

Q26 If x² + 1/4x² = 8, find x³ + 1/8x³ .

Q27 If a²
- 3a + 1 = 0, find (i) a² + 1/a²
(ii) a³ + 1/a³ .

Q28 If a = 1/ (a - 5), find
(i) a - 1/a
(ii) a + 1/a
(iii) a²
- 1/a² .

Q29 If (x + 1/x)² = 3, find x³ + 1/x³ .

Q35 If a - b = 7 and a² + b² = 85, then find the value of a³ - b ³