Question

compute the value of 9x²+4y² if xy=6 and 3x+2y=12​

Answer 1

Answer:

72

Step-by-step explanation:

$9 {x}^{2} + 4 {y}^{2}$

$( {3x)}^{2} + ( {2y)}^{2} + 2(3x)(2y) - 2(3x)(2y)$

${(3x + 2y)}^{2} - 12xy$

put values

${(12)}^{2} - 12(6)$

$144 - 72$

$72$

Answer 2

.

We have xy = 6

Given

3x + 2y = 12

Sqauring both sides

(3x + 2y )² = 12²

9x² + 4y² + 12xy = 144

9x² + 4y² + 12× 6 = 144

9x² + 4y² = 144 - 72 = 72

9x² + 4y² = 72

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