Solve (x-2)^3 = x^3 - 2(x−2)3=x3−2?

1 Answer
Nityananda
Oct 31, 2017

1

Explanation:

Given,(x-2)^3=x^3-2(x−2)3=x3−2
rArr x^3-3x^2. 2+3x.2^2-2^3=x^3-2⇒x3−3x2.2+3x.22−23=x3−2
rArr x^3-x^3-6x^2+12x-8+2=0⇒x3−x3−6x2+12x−8+2=0
rArr -6x^2+12x-6=0⇒−6x2+12x−6=0
rArr -6(x^2-2x+1)=0⇒−6(x2−2x+1)=0
rArr x^2-2x+1=0 ⇒x2−2x+1=0[divide both sides by -6]
rArr (x-1)^ 2 = 0⇒(x−1)2=0
rArr x-1 = 0⇒x−1=0[squaring both sides]
rArr x = 1⇒x=1

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