Question

if a + b + c equal to 3 x find x minus a whole cube + x minus b whole cube + x minus C whole cube minus 3 into x minus A into x minus b into x minus C​

Answer 1

Step-by-step explanation:

a+b+c = 3x.... Proved.

Step-by-step explanation:

We are given that

...... (1)

And, we have to prove that, ...... (2)

Now we will prove it.

From equation (1), by simplification we get,

(x³-3x²a+3xa²-a³)+(x³-3x²b+3xb²-b³)+(x³-3x²c+3xc²-c³)=3(x-a)(x²-cx-bx+bc)

⇒(x³-3x²a+3xa²-a³)+(x³-3x²b+3xb²-b³)+(x³-3x²c+3xc²-c³)=3(x³-x²c-x²b+xbc-x²a+xac+xab-abc)

Cancelling equal terms from both sides we get,

⇒3x(a²+b²+c²)-(a³+b³+c³) =3x(ab+bc+ca)-3abc

⇒3x(a²+b²+c²-ab-bc-ca)= a³+b³+c³-3abc

We know the equation, a³+b³+c³-3abc= (a+b+c)(a²+b²+c²-ab-bc-ca)

⇒3x(a²+b²+c²-ab-bc-ca)= (a+b+c)(a²+b²+c²-ab-bc-ca)

⇒3x= a+b+c

⇒a+b+c = 3x

Hence proved.