Question

If3+4y = 16 and xy=4 , find the value of 9x2+16y2

Answer 1

Step-by-step explanation:

given equations are

3x + 4y = 16 —>1st eqn.

xy = 4 ——->2nd eqn.

We can write 2nd equation as follows

By multiplying 12 on both sides

3x . 4y =12 * 4

12xy = 48 —->3rd eqn.

Now take 1st eqn and squaring on both sides we get

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

9x^2 + 16y^2 + 2(3x)(4y) = 256

9x^2 + 16y^2 + 2(12xy) = 256

Substitute 12xy = 48 In above eqn.

9x^2 + 16y^2 +2(48) = 256

9x^2 + 16y^2 +96 = 256

9x^2 + 16y^2 = 256 - 96

9x^2 + 16y^2 = 160

Answer 2

Answer:

3x + 4y = 16 —>1st eqn. xy = 4 ——->2nd eqn. 12xy = 48 —->3rd eqn. Substitute 12xy = 48 In above eqn