The number of real solutions of `|x|+2sqrt(5-4x-x^2)=16`is/area. 6b. 1 c.0 d. 4
A. 6
B. 1
C. 0
D. 4
A. 6
B. 1
C. 0
D. 4
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Correct Answer – 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.