Question

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

Answer 1

Answer: $9x^2 + 4y^2 = 72$

Step-by-step explanation:

Given:

$3x + 2y = 12$

$xy = 6$

To find:

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

Solution:

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

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

$9x^2 + 4y^2 = (3x+2y)^2 - 12xy$

Now, put 3x+2y = 12 and xy = 6 in this equation

$9x^2 + 4y^2 = (12)^2 - 12(6)$

$9x^2 + 4y^2 = 144 - 72$

$9x^2 + 4y^2 = 72$

∴ $9x^2 + 4y^2 = 72$

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