Question

Verify that x cube + y cube + z cube minus 3 x y z is equal to 1 by 2 x + y + z x minus y whole square + y - z whole square + z - x whole square

Answer 1

Answer:

x³+y³+z³-3xyz=1/2(x+y+z)(x-y)²+(y-z)²+(z-x)²

now let x³+y³+z³-3xyz be p(x)

So ,

p(x)=1/2(x+y+z)(x-y)²+(y-z)²+(z-x)²

• p(x)=1/2(x+y+z)(x²-2xy+y²)+(y²-2yz+z²)+(z²-2zx+x²)

:p(x)=1/2(x+y+z)(x²+x²+y²+y²+z²+z²-2xy-2yz-2zx)

:p(x)=1/2(x+y+z)(2x²+2y²+2z²-2xy-2yz-2zx)

:p(x)=1/2(x+y+z)2(x²+y²+z²-xy-yz-zx) (after canceling 2 by 2 in ½×2 we get

:p(x)=(x+y+z)(x²+y²+z²-xy-yz-zx)

so according to the formula x³+y³+z³-3xyz=(x+y+z)(x²+y²+z²-xy-yz-zx)

Answer 2

Ncert class 9th ex 2.5 question number 12