Question

If 3x+ 4y= 16 and xy = 4. find the value of:

9x2+ 16y2​

Answer 1

Answer:

Given that ( 3x + 4y ) = 16 and xy = 4

We need to find 9x2 + 16y2.

We know that

( a + b )2 = a2 + b2 + 2ab

Consider the square of 3x + 4y :

∴ ( 3x + 4y )2 = (3x)2 + (4y)2 + 2 x 3x x 4y

⇒ ( 3x + 4y )2 = 9x2 + 16y2 + 24xy

( 3x + 4y )2 = 9x2 + 16y2 + 24xy

⇒ (16)2 = 9x2 + 16y2 + 24(4)

⇒ 256 = 9x2 + 16y2 + 96

⇒ 9x2 + 16y2 = 160

Answer 2

3x + 4y = 16 and xy is 4

x=4 , y=1

9x2 + 16y2 = [9*4*2 = 72] + [ 16*1*2 = 32]

72+32=104