Let R and let the equation E be | x |^2-2| x |+| -3|=0. Then the … - Vidyadip

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 $..........$

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Answer

c
$| x |^2-2| x |+|\lambda-3|=0$

$| x |^2-2| x |+|\lambda-3|-1=0$

$(| x |-1)^2+|\lambda-3|=1$

At $\lambda=3, x =0$ and 2 ,

at $\lambda=4$ or 2 , then

$x =1 \text { or }-1$

So maximum value of $x+\lambda=5$

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