Question

if 3x+4y=16and xy=9 find the value of 9x^2+16y^2​

Answer 1

Answer:

3x+4y=16 (given)

Squaring both sides

=> (3x+4y)^2 = (16)^2

=> (3x+4y)^2= 256........(1)

we know that (a+b)^2= a^2+b^2+2ab

using identity in equation (1)

(3x)^2 + (4y)^2 + 2 × 3x × 4y = 256

9x^2 + 16y^2 + 24xy = 256 (given xy=9)

9x^2 + 16y^2 + 24×9= 256

9x^2 + 16y^2 +216= 256

9x^2 + 16y^2 =256-216

9x^2 + 16y^2= 40

your answer is 40