Question

Solve `(x-2)^3 = x^3 - 2`?

Answer 1

1

Explanation:

Given,`(x-2)^3=x^3-2`
`rArr x^3-3x^2. 2+3x.2^2-2^3=x^3-2`
`rArr x^3-x^3-6x^2+12x-8+2=0`
`rArr -6x^2+12x-6=0`
`rArr -6(x^2-2x+1)=0`
`rArr x^2-2x+1=0`[divide both sides by -6]
`rArr (x-1)^ 2 = 0`
`rArr x-1 = 0`[squaring both sides]
`rArr x = 1`