Question

If 3x-4y=10 and xy=-1,find the value of 9xsq +16ysq

Answer 1

9x²+16y²
=(3x)²+(4y)²
=(3x-4y)²+2*3x*4y
=(10)²+24*-1 [given]
=100+(-24)
=100-24
=76
hope this answer helps you

Answer 2

3x-4y=10 
⇒(3x-4y)² = 10²  (squaring boths sides)
⇒9x² + 16y² -24xy = 100
⇒9x² + 16y² = 100 + 24xy    
⇒9x² + 16y²  = 100 - 24                 [xy = -1, given]
⇒9x² + 16y²  = 76

∴9x² + 16y²  = 76

I hope this helps you ^_^