Question

If a + β + γ = 0, show that 3(a 2 + β 2 + γ 2 )(a 5 + β 5 + γ 5 ) = 5(a 3 + β 3 + γ 3 )(a 4 + β 4 + γ 4 )

Answer 1

Hence , proved.

It is so simple proving question.

Answer 2

Firstly,
Left hand side,
=3(a2+B2+y2) (a5+B5+y5)
Now taking 2 and 5 common
=3*2*5(a+B+y) (a+B+y)
=30*0*0 (a+B+y=0)
=0.
Now-taking right hand side,
=5(a3+B3+y3) (a4+B4+y4)
Now we will take 3 and 4 as common
=5*3*4(a+B+y) (a+B+y)
=60*0*0. (a+B+y=0)
=0
Hence proved
L.H.S=R.H.S



I hope it’s useful for you.