I wt yt z = 0I then brove that :wº + y + z3 = Bryz

1.	I wt yt z = 0I then brove that :wº + y + z3 = Bryz
Answer» Given,x+y+z=0x+y+z=0. Consider the identity, (x3+y3+z3−3xyz)=(x+y+z)(x2+y2+z2−xy−yz−zx)(x3+y3+z3−3xyz)=(x+y+z)(x2+y2+z2−xy−yz−zx). Substitutex+y+z=0x+y+z=0in above identity. x3+y3+z3−3xyz=0×(x2+y2+z2−xy−yz−zx)x3+y3+z3−3xyz=0x3+y3+z3=3xyzx3+y3+z3−3xyz=0×(x2+y2+z2−xy−yz−zx)x3+y3+z3−3xyz=0x3+y3+z3=3xyz Hence, it is proved thatx3+y3+z3=3xyz 3xyz is the right answer

Answer»

Given,x+y+z=0x+y+z=0.

Consider the identity,

(x3+y3+z3−3xyz)=(x+y+z)(x2+y2+z2−xy−yz−zx)(x3+y3+z3−3xyz)=(x+y+z)(x2+y2+z2−xy−yz−zx).

Substitutex+y+z=0x+y+z=0in above identity.

x3+y3+z3−3xyz=0×(x2+y2+z2−xy−yz−zx)x3+y3+z3−3xyz=0x3+y3+z3=3xyzx3+y3+z3−3xyz=0×(x2+y2+z2−xy−yz−zx)x3+y3+z3−3xyz=0x3+y3+z3=3xyz

Hence, it is proved thatx3+y3+z3=3xyz

3xyz is the right answer

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