Question

if x+y+1=0 prove that x²+y²+1=3xy

Answer 1

if x+y+1=0 prove that x²+y²+1=3xy

SOLUTION : -

→ here, we have x + y + 1 = 0

then, x + y = -1............( Equ 1 )

By Taking cube on both the sides, we get

( x + y ) ³ = ( -1 )³

→ x ³ + y ³ + 3x² y + 3xy² = -1

→ x ³ + y ³ + 3xy ( x+ y ) = -1

→ x³ + y ³ + 3xy(-1) = -1

Therefore, by using ( Equ 1 ) ,we get ;

→ x³ + y ³ + 1 = 3xy

hence , proved