if 3x=a+b+c then find (x-a) cube + x-b whole cube + x-c whole cube - 3(x-a)(x-b)(x-c) =?
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given,
a+b+c=3x
=>3x-a-b-c=0.......(i)
let, p=x-a;q=x-b;r=x-c
therefore,
p+q+r=x-a+x-b+x-c
=3x-a-b-c
=0 [from (i)]
therefore, the given expression is---
p^3+q^3+r^3-3pqr
=(p+q+r)(p^2+q^2+r^2-pq-qr-rp)
=0(p^2+q^2+r^2-pq-qr-rp)
=0
a+b+c=3x
=>3x-a-b-c=0.......(i)
let, p=x-a;q=x-b;r=x-c
therefore,
p+q+r=x-a+x-b+x-c
=3x-a-b-c
=0 [from (i)]
therefore, the given expression is---
p^3+q^3+r^3-3pqr
=(p+q+r)(p^2+q^2+r^2-pq-qr-rp)
=0(p^2+q^2+r^2-pq-qr-rp)
=0
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