Question

If 3x-4y=10 and xy= -1 , find the value of 9x²+16y²

Answer 1

$( {3x - 4y})^{2} = {9x}^{2} - 2 \times 3x \times - 4y + {16y}^{2} \\ 100= {9x}^{2} + {16y}^{2} + 24xy \\ 100 = {9x}^{2} + {16y}^{2} - 24 \\ 100 + 24 = 124 = {9x}^{2} + {16y}^{2}$

Answer 2

$\huge\bold\star\red{Solution}\star$

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$(3x - 4y)^{2} = (3x)^{2} - 2.3x.4y + (4y)^{2} = 9x^{2} - 24xy + 16y^{2}$

$(3x - 4y)^{2} = 9x^{2} + 16y^{2} - 24xy$

$(10)^{2} = 9x^{2} + 16y^{2} - 24 \times ( - 1)$

$100 = 9x^{2} + 16y^{2} + 24$

$9x^{2} + 16y^{2} = 100 - 24 = 76$

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