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Find all the values of the parameter a for which the inequality 4 x - a2 x -a+3≤0 is satisfied by at least one real x.

Find all the values of the parameter a for which the inequality 4- a2x -a+3≤0 is satisfied by at least one real x.

Grade:12th Pass

1 Answers

Chetan Mandayam Nayakar
312 Points
10 years ago

let 2x=y, y is always non-negative, a≥(y^2 +3)/(y+1) =f(y), f(y) is minimum when 2y(y+1)=y^2 +3, y=1 (y=-3 is ruled out because y=2^x is never negative for real x), f(1)=2, therefore answer is a≥2

 

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