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Number of real solutions of sqrt(2x-4)-s...

Number of real solutions of `sqrt(2x-4)-sqrt(x+5)=1` is (a) 0 (b) 1 (c) 2 (d) infinite

A

`0`

B

`1`

C

`2`

D

infinite

Text Solution

Verified by Experts

The correct Answer is:
B
`(b)` We have `sqrt(2x-4)=1+sqrt(x+5)`
Squaring
`2x-4=1+(x+5)+2sqrt(x+5)`
`implies x-10=2sqrt(x+5)`
`implies x^(2)+100-20x=4x+20`
`impliesx^(2)-24x+80=0`
`impliesx=4,20`
Putting `x=4`, we get `sqrt(4)-sqrt(9)=1`, which is not possible
Putting `x=20`, we get `sqrt(36)-sqrt(25)=1`
Hence, `x=20` is the only solution.
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