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

Answer 2

Hi friend,

Your question might be as follows:-

If x+y+1=0 prove that x³+y³+1=3xy

x+y+1 = 0

We know that,

(a³+b³+c³) - 3abc = (a+b+c) (a²+b²+c²-ab-bc-ca)

Apply the principle,

(x³+y³+1³) - 3(x)(y)(1) = (x+y+1) (x²+y²+1²-(x)(y)-(y)(1)-(1)(x))

(x³+y³+1) -3xy = 0 (x²+y²+1²-(x)(y)-(y)(1)-(1)(x))

(x³+y³+1) - 3xy = 0

(x³+y³+1) = 3xy

Hence proved.

Hope it helps