If 0<a<5, 0<b<5 and x^2+5 2 =x-2 (a+bx) is satisfied for at least one real x then the greatest value of a+b is

JEE Advanced Mathematics question

If , and is satisfied for at least one real then the greatest value of is

Answer: (C)

2(a+bx)=x-=-=-=-2--2 .

But . So equality is forced: and , i.e.

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Question ID VK-108033