x square+1) (ysquare+1)+16=8(x+y) find (xcube+ycube)
Answers
Answered by
17
if (x^2+1)(y^2+1)+16=8(x+y) , then find x^3+y^3
(x² + 1)(y² + 1) + 16 = 8(x+y)
=> x²y² + 1 + x² + y² + 16 = 8(x + y)
=> x²y² + 1 - 2xy + 2xy + x² + y² + 16 -8(x + y) = 0
=> (xy - 1)² + (x + y)² + 16 - 8(x+y) = 0
=> (xy -1)² + (x + y - 4)² = 0
as square can not be negative
=> (xy -1)² = 0 & (x + y - 4)² =0
=> xy = 1 & x + y = 4
x³ + y³ = ( x+ y)³ -3xy(x+y)
=> x³ + y³ = 4³ - 3(1)(4)
=> x³ + y³ = 64 - 12
=> x³ + y³ = 52
Answered by
0
Answer:
52
Step-by-step explanation:
Similar questions