Q3 of 65 Page 145

Short answer type questions:

Let us write the value of (x – a)3 + (x – b)3 + (x – c)3 – 3(x – a) (x – b) (x – c) if 3x = a + b + c.

As we know the identity that,


If l + m+ n = 0, then l3 + m3 + n3 – 3mnl = 0


Let p = (x - a), q = (x - b), r = (x – c)


p + q + r = (x – a + x – b + x – c) = 3x – a – b – c


also It is given 3x = a + b + c,


⇒ p + q + r = 0


⇒ p3 + q3 + r3 – 3pqr =0


On substituting the values of p, q and r in above equation, we get,


(x – a)3 + (x – b)3 + (x – c)3 – 3(x – a) (x – b) (x – c) = 0


∴ the required value is 0.


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