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Mathematics · 2023

JEE Main · 13 April 2023, Shift 2 · Q4

If the system of equations 2 x+y-z=5; 2 x-5 y+λ z=μ; x+2 y-5 z=7 has infinitely many solutions, then (λ+μ)^2+(λ-μ)^2 is equal to

If the system of equations $$\begin{aligned} & 2 x+y-z=5 \\ & 2 x-5 y+\lambda z=\mu \\ & x+2 y-5 z=7 \end{aligned} $$ has infinitely many solutions, then $\displaystyle (\lambda+\mu)^2+(\lambda-\mu)^2$ is equal to
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JEE Main 2023 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.