Question 39
Find the value of:
(i) $x^{3} + y^{3} - 12 x y + 64$ , when x + y = - 4

(ii) $x^{3} - 8 y^{3} - 36 x y - 216$ , when x = 2y + 6

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Solution

(i) Given
x + y + 4 = 0
$∴ x^{3} + y^{3} + (4)^{3} = 3 x y (4)$ …….(1)
$[U s i n g t h e i d e n t i t y, i f a + b + c = 0, t h e n a^{3} + b^{3} + c^{3} = 3 a b c$ ]
$= 12 x y$
Now,
$x^{3} + y^{3} - 12 x y + 64 = x^{3} + y^{3} + 64 - 12 x y$
$= 12 x y - 12 x y = 0$ [from Eq. (i) ]

(ii) Given,
$x - 2 y - 6 = 0$
$∴ x^{3} + (- 2 y)^{3} + (- 6)^{3} = 3 x (- 2 y) (- 6)$
$[U s i n g t h e i d e n t i t y, i f a + b + c = 0, t h e n a^{3} + b^{3} + c^{3} = 3 a b c$ ]
$x^{3} - 8 y^{3} - 216 = 36 x y$ …..(i)
Now, $x^{3} - 8 y^{3} - 36 x y - 216$
$= x^{3} - 8 y^{3} - 216 - 36 x y$
$= 36 x y - 36 x y = 0$ [from Eq. (i)]

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Question 39
Find the value of:
(i) $x^{3} + y^{3} - 12 x y + 64$ , when x + y = - 4

(ii) $x^{3} - 8 y^{3} - 36 x y - 216$ , when x = 2y + 6

x^{3} - 8 y^{3} - 36 x y - 216

x = 2 y + 6

x = 2 y + 6

x^{3} - 8 y^{3} - 36 x y - 216

x^{3} + y^{3} - 12 x y + 64,

x + y = - 4.

x^{3} + y^{3} - 12 x y + 64

x + y = 4

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