Question

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1. If 3x+2y=12 and xy = 6 , find the value of 9x²+4y².


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Answer 1

$ans$

3x +2y =12

squaring both side

9x² + 4y²+ 2× 3x× 2y =144

9x²+4y² = 144 - 12xy

9x²+4y²= 144 - 12 × 6

since, xy = 6

9x²+4y² = 144-72 = 72

therefore , 9x²+4y² = 72 ans

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Answer 2

Answer:

72 is the answer.

Step-by-step explanation:

Here we shall use the identity,

${(a + b)}^{2} = {a}^{2} + {b}^{2} + 2ab \\ {a}^{2} + {b}^{2} = {(a + b)}^{2} - 2ab$

So,

$9{x}^{2} + 4 {y}^{2} ={(3x)}^{2} + {(2y)}^{2} \\ = {(3x + 2y)}^{2} - 2(3x)(2y) \\ ={(3x + 2y)}^{2} -12xy \\ = {(12)}^{2} - 12 \times 6 \\ = 144 - 72 \\ = 72$

I hope it helps.

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