Question

The sum of squares of real roots of the equation: \(x^2+|2 x-3|-4=0,\) is

(1) \(6(2-\sqrt{2})\)

(2) \(3(2-\sqrt{2})\)

(3) \(3(2+\sqrt{2})\)

(4) \(6(2+\sqrt{2})\)

Answer 1

Correct option is (1) \(6(2-\sqrt{2})\)  

\(x^2+|2 x-3|-4=0\)  

\(\Rightarrow \text{two roots are}\ x=-\sqrt{2}+1,2 \sqrt{2}-1\)  

\(\Rightarrow \text{Sum of squares} =12-6 \sqrt{2}=6(2-\sqrt{2})\)