If the system of equation 2 x-y+z=0, x-2 y+z=0 and a x-y+2 z=0 has infinitely many solutions and f(x) be a continuous function such that f(5+x)+f(x)=2 x R , then ₀^ -2 a f(x) d x is equal to:

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Quantrex Academy · Accepted Answer

Correct answer: B. -2 a

aligned & =0, a=5 & ₀⁻¹⁰ f(x) d x= ₀⁻⁵ f(x) d x+ _ -5 ⁻¹⁰ f(x) d x= _ -5 ⁻¹⁰ f(x+5) d x+ _ -5 ⁻¹⁰ f(x) d x=2 _ -5 ⁻¹⁰ d x=-10 aligned

If the system of equation 2 x-y+z=0, x-2 y+z=0 and a x-y+2 z=0 has infinitely many solutions and f(x) be a continuous function such that f(5+x)+f(x)=2 x R , then ₀^ -2 a f(x) d x is equal to:

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