Compute the value of 9x^2 + 4y^2 if xy = 6 and 3x + 2y = 12.

Question

asked Aug 7, 2022 11.2k views

1 Answer

Marc Seeger · Answer 1 · 2022-08-11T10:10:05+0000

Answer:

Consider the equation 3x + 2y = 12

Now, square both sides:

(3x + 2y)^2 = 122

=> 9x^2 + 12xy + 4y^2 = 144

=>9x^2 + 4y^2 = 144 – 12xy

From the questions, xy = 6

So,

9x^2 + 4y^2 = 144 – 72

Thus, the value of 9x^2 + 4y^2 = 72

Answered by GAUTHMATH