Question

If 2x+3y=13 and xy =6, find the value of 8x cube +27y cube

Answer 1

8x^3 + 27y^3

=(2x)^3 + (3y)^3

From a^3 + b^3 = (a + b) (a^2 - ab + b^2) , where a = 2x and b = 3y

Therefore,

(2x)^3 + (3y)^3 = (2x + 3y) (4x^2 - 6xy + 9y^2)

= 13 (4x^2 + 9y^2 - 36)

Squaring 2x + 3y = 13

We get,

4x^2 + 9y^2 +12xy = 169

Therefore, 4x^2 + 9y^2 = 169 - 72

= 97

Putting value in earlier equation, we get,

8x^3 + 27y^3 = 13 (97 - 36)

= 13 * 61

= 793 Answer.... ok follow me ✌️ samile ✌

Answer 2

Answer:

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