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The number of real solutions of |x|+2sqr...

The number of real solutions of `|x|+2sqrt(5-4x-x^2)=16` is/are a. 6 b. 1 c. 0 d. 4

A

6

B

1

C

0

D

4

Text Solution

Verified by Experts

The correct Answer is:
3
We have
`2sqrt(5 - 4x - x^(2)) = 16 - |x|`
`rArr 4(5 - 4x - x^(2)) = 256 - 32|x| + x^(2)`
`rArr 5x^(2) - 32|x| + 16x + 236 = 0`
`rArr 5x^(2) - 16x + 236 = 0`, when `x ge 0`
and `5x^(2) + 48x + 236 = 0`, when `x lt 0`.
In both cases, equation has non-real roots.
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