Question

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

Answer 1

Answer:

The value of $9x^2+4y^2$ is 72

Step-by-step explanation:

Formula used:

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

This implies

$a^2+b^2=(a+b)^2-2ab........(1)$

$Now,\\\\9x^2+4y^2\\\\=(3x)^2+(2y)^2\\\\=(3x+2y)^2-2(3x)(2y)\:\:\:(using(1))\\\\=(3x+2y)^2-12(xy)\\\\=(12)^2-12(6)\\\\=144-72\\\\=72$

Answer 2

Answer:

72

Step-by-step explanation:

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

Consider the equation 3 x + 2 y = 12

             3 x + 2 y = 12  squaring both sides we get

           (3 x + 2 y)^2 = 12^2

      Using the formula (a + b)^2 = a^2 + b^2 + 2 ab we get

        9 x^2 + 4 y^2 + 2 . 3 x . 2 y = 144

       9 x^2 + 4 y^2 + 12 (x y) = 144

      Given x y = 6

 So  9 x^2 + 4 y^2 + 12 (6) = 144

        9 x^2 + 4 y^2 = 144 - 72

      9 x^2 + 4 y^2 = 72