If 3x + 2y = 9 and Xy = 3, Find : 27x3 + 8y3.

If 3x + 2y = 9 and xy = 3, find : 27x³ + 8y³.

Sum

27x³ + 8y³ = (3x)³ + (2y)³

= (3x + 2y)³ − 3.3x . 2y (3x + 2y)

= (3x − 2y)³ − 18xy (3x + 2y)

= (9)³− 18(3) (9)

= 729 − 486

= 243

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Application of Formulae

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Chapter 12: Identities - Exercise 12 (D) [Page 155]

Chapter 12 Identities
Exercise 12 (D) | Q 14 | Page 155

If a² + b² = 29 and ab = 10, find : a + b

If a² + b²= 10 and ab = 3; find : a – b

If `"a" - 1/"a"=4`, find : `"a"^2+1/"a"^2`

Find: a² + b² + c², if a + b + c = 9 and ab + bc + ca = 24

Find : a + b + c, if a² + b² + c² = 83 and ab + bc + ca = 71.

If `2"x"-1/(2"x")=4`, find : `4"x"^2+1/(4"x"^2)`

If a + b + c = 9 and ab + bc + ca = 15, find: a² + b² + c².

If 3x – 4y = 5 and xy = 3, find : 27x³ – 64y³.

If a + b = 8 and ab = 15, find a³ + b³.

If 5x – 4y = 7 and xy = 8, find : 125x³ – 64y³.