Question

14. If 3x + 4y = 16 and xy = 4; find the value of 9x2 + 16y2​

Answer 1

Answer:

Step-by-step explanation:

Given that,

3x + 4y = 16 and xy = 4.

Now we take 3x + 4y = 16, we have

Squaring on both sides, we get

(3x + 4y ) whole square = (16) whole square

(3x )whole square + (4y)whole square + 2 × 3x × 4y = 256 [∵ (a +b)whole square = a square+ b square +2ab]

9x square + 16y square + 24xy = 256

9x square + 4y square + 24 × 4= 256 ( ∵ xy = 4 )

9x square + 4y square + 96 = 256

9x square + 4y square = 256 - 96

9x square + 4y square = 160 is the answer.