Solve sqrt(5+x) + sqrt(x) = 5?

Question

Please show working out. I've been trying to do this for so long but just can't seem to get it. I know the answer is x=4 by just looking at the question.

Thanks

Answer 1

Domain: 5 + x>=0 and x >=0
x>=-5 and x>=0, therefore x>=0

sqrt(5+x)=5 - sqrt(x) square both sides
5+x = 25 - 10sqrt(x) + x
5 + x - 25 - x = -10sqrt(x)
-20 = -10sqrt(x)
2 = sqrt(x) square both sides again
4 = x

Check the answer and you are done :-)

Answer 2

First, transfer sqrt x to the other side:

sqrt (5+x) = 5 - sqrt x

Square both sides:

5 + x = 25 + x - 10 sqrtx
-20 = - 10 sqrtx
2 = sqrt x

Square both sides:

x = 4

Answer 3

Take the square of both sides:
[sqrt(5+x) + sqrt(x) ]² = 25

Now multiply out the square:
sqrt(5+x)² + 2sqrt(5+x)sqrt(x) + sqrt(x)² = 25

5+2x + 2sqrt(5+x)sqrt(x) = 25

2x + 2sqrt(5+x)sqrt(x) = 20
x + sqrt(5+x)sqrt(x) = 10

x + sqrt(5x + x²) = 10
sqrt(5x + x²) = 10 - x

Again square both sides:
5x + x² = 10² - 20x + x²

25x = 100
x = 4

Answer 4

sqrt(5+x) + sqrt(x) = 5
first, isolate one system with the sqrt sign.

sqrt(5+x) = 5 - sqrt(x)

then square both sides.

5+x = 25-10sqrt(x)+x

simplify, you get.

10sqrt(x) = 20

divide both sides by 10.

sqrt(x) = 2

square both sides again.

x = 4

:D

Answer 5

I'm glad i graduated high school in 1981!