Question

Let $\lambda \in R$ and let the equation $E$ be $|x|^2-2|x|+|\lambda-3|=0$. Then the largest element in the set $S=$ \\{x+\lambda: x is an integer solution of E\\} is

Answer 1

The correct answer is 5.
∣x∣2−2∣x∣+∣λ−3∣=0
∣x∣2−2∣x∣+∣λ−3∣−1=0
(∣x∣−1)2+∣λ−3∣=1
At λ=3,x=0 and 2 ,
at λ=4 or 2 ,
then x=1 or −1
So maximum value of x+λ=5