Q.

If the system of equations
 2x+yz=52x5y+λz=μx+2y5z=7
has infinitely may solutions, then (λ+μ)2+(λμ)2 is equal to

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a

916

b

904

c

920

d

912

answer is C.

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Detailed Solution

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2x+yz=52x5y+λz=μx+2y5z=76y(λ+1)z=5μ & y3z=361=λ+13=5μ3λ+1=18λ=17,18=5μμ=13 (λ+μ)2+(λμ)2=42+302=916

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