SAMPLE QUESTIONS FOR SA1 (9TH)

Q. If x+y+z=0,   show that x³+y³+z³=3xyz.
Sol:
Given,
=>x+ y+ z=0
=>x+ y = - z_______(1)
=>(x+y)³=( - z)³
=>x³+y³ - 3xy(x+y)= - z³
=>x3+y³ - 3xy( - z)= - z³  [from eqn (1)]
=>x³+y³ - 3xyz= - z³
=>x³+y³+z³=3xyz