Question

if 3x-2y=10andxy=16 find the value of 27xsquare-8ysquare..
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Answer 1

Answer:

The value is -404 (OR) 696

Step-by-step explanation:

3x - 2y = 10 .... (1)

xy = 16 .... (2)

From (2)

y = 16/x

(1) = 3x - 2(16/x) = 10

= 3x^2 - 10x - 32 = 0

= 3x^2 - 16x + 6x - 32 = 0

= x(3x - 16) + 2(3x - 16) = 0

= (x + 2)(3x - 16) = 0

Therefore,

x = -2 (OR) x = 16/3

Similarly,

y = -8 (OR) y = 3

Case 1

27x^2 - 8y^2

= 27(-2)^2 - 8(-8)^2

= 108 - 512

= -404

Case 2

27x^2 - 8y^2

= 27(16/3)^2 - 8(3)^2

= 768 - 72

= 696