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Algebra> inequality...

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the possible values of a for which e^2x-(a-2)e^x+a<0 holds for atleast one x bbelongs to (0,infinity) are-

(a)6 (b)9 (c)12 (d)16

shefali sharma , 16 Years ago

Grade 12

1 Answers

Jitender Singh

Ans:
Hello Student,
Please find answer to your question

e^2x– (a-2)e^x+ a < 0
Let
t = e^x
t²– (a – 2)t + a < 0
So the equation does not real roots.
(a – 2)²< 4a
a²+ 4 – 4a < 4a
a²– 8a + 4 < 0
$a = \frac{8\pm \sqrt{48}}{2}$
$a = \frac{8\pm 4\sqrt{3}}{2}$
$a = 4\pm 2\sqrt{3}$
$\Rightarrow a\in (4-2\sqrt{3}, 4 + 2\sqrt{3})$
So 6 is the correct option.

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