Question

if a+b+c=3x, then find the value of (x-a)^3+(x-b)^3+(x-c)^3​

Answer 1

Solution :-

(x - a)³ + (x - b)³ + (x - c)³

We know that

If p + q + r = 0 then p³ + q³ + r³ = 3qr

Here

• p = (x - a)
• q = (x - b)
• r = (x - c)

p + q + r

= (x - a) + (x - b) + (x - c)

= x - a + x - b + x - c

= 3x - a - b - c

= 3x - (a + b + c)

= 3x - 3x

[ Because a + b + c = 3x ]

= 0

Therefore p + q + r = 0

So, (x - a)³ + (x - b)³ + (x - c)³

= 3(x - a)(x - b)(x - c)

Hence, then find the value of (x-a)³ + (x-b)³ + (x-c)³ is 3(x - a)(x - b)(x - c).