Question

Find the value of (x-a)³+(x-b)³(x-c)-3(x-a)(x-b)(x-c),when a+b+c=3x.
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Answer 1

Explanation:

We know that, m3 + n3 + l3 - 3mnl = 0, if m + n + l = 0.  ... (i)

 

 

(x-a)³+(x-b)³+(x-c)³-3(x-a)(x-b)(x-c)

 

Here,  

m = x - a, n = x - b and l = x - c  

m+n+l = x - a + x - b + x - c = 3x - (a + b + c) = 3x - 3x = 0....(a + b + c = 0)

 

→ (x-a)³+(x-b)³+(x-c)³-3(x-a)(x-b)(x-c) = 0  .. from (i)