Question

The sum of squares of roots of \(|x-2|^{2}-|x-2|-2=0 \) and \(x^{2}-2|x-3|-5=0\) equals to

Answer 1

Answer is: 42  

\(|x-2|^{2}-|x-2|-2=0\)

Let |x - 2|=t

\(t^{2}-t-2=0\)

\(t^{2}-2 t+t-2=0\)

\(t(t-2)+1(t-2)=0\)

\((t+1)(t-2)=0\)

t = -1, t = 2

\(\therefore\ |x-2|=-1, \quad|x-2|=2\)

Number + possible \(\Rightarrow x - 2= \pm 2\)

\(\Rightarrow x=0,4\)

\(x^{2}-2|x-3|-5=0\)

when x < 3

\(x^{2}+2(x-3)-5=0\)

\(x^{2}+2 x-11=0\)