Question

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

Answer 1

SOLUTION

GIVEN

3x - 4y = 10 and xy = -1

TO DETERMINE

The value of 9x² + 16y²

EVALUATION

$3x - 4y = 10$

Squaring both sides we get

${(3x - 4y)}^{2} = {10}^{2}$

$\implies \: 9 {x}^{2} + 16 {y}^{2} - 24xy = 100$

$\implies \: 9 {x}^{2} + 16 {y}^{2} - 24 \times ( - 1) = 100$

$\implies \: 9 {x}^{2} + 16 {y}^{2} = 100 - 24$

$\implies \: 9 {x}^{2} + 16 {y}^{2} = 76$

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