Question

If 2x + 3y = 11 and xy = 3, find the value of 4x^2 + 9y^2.

Answer 1

Answer:

2x+3y=11

squaring both sides

(2x+3y)^2=11^2

4x^2 + 9y^2+ 2(2x)(3y)=121

4x^2+9y^2+12xy=121

4x^2+9y^2+12(3)=121

4x^2+9y^2+36=121

4x^2+9y^2=85.........

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Answer 2

$given \\ 2x + 3y = 11 \\ and \: xy = 3 \\ so \: now \\ (2x + 3y) ^{2} = (2x) ^{2} + {(3y)}^{2} + 2 \times 2x \times 3y \\ (11) ^{2} \: \: \: \: \: \: \: \: \: \: \: = 4x ^{2} + 9y ^{2} + 12xy \\ 121 \: \: \: \: \: \: \: \: \: \: \: \: \: \: = 4x ^{2} + 9y ^{2} + 12(3) \\ 121 \: \: \: \: \: \: \: \: \: \: \: \: \: \: = {4x}^{2} + {9}^{2} + 36 \\ {4x}^{2} + {9y}^{2} \: = 121 - 36 \\ {}$

hence, the value of 4x²+9y²=85

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