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

Question

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

Aicharya · Accepted Answer

Given: | x | 2 - 2 | x | + | &#955; - 3 | = 0 &#8658; | &#955; - 3 | = x 2 - x At &#955; = 3 , x = 0 and 2 , At &#955; = 4 or 2 , then, x = 1 or - 1 So, maximum value of x + &#955; = 5 when x = 1 and &#955; = 4 .

Let $\lambda \in \mathbb{R}$ and let the equation $E$ be $|x|^2 - 2|x| + |\lambda - 3| = 0$. Then the…

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