Equations Reducible to Quadratics (1 Viewer)

[vaaan]

Yeaah; I'm having trouble with this question.

sqroot(5+x) + sqroot(x) = 5

Solve for x.

Your help will be greattllyy appreciated.

 

[study-freak]

square both sides
5+x+x+2sqrt(x^2+5x)=25
sqrt(x^2+5x)=10-x
x^2+5x=100+x^2-20x
25x=100
x=4

 

[vaaan]

....
oooohhh.

LOL. I get it. Ty.

 

[annabackwards]

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

Squaring both sides

5+x = 25 - 10sqrt(x) + x
- 10sqrt(x) = - 20
sqrt(x) = 2
x = 4

 

[Aerath]

I thought reducible to quadratic was something like (x+2)^2 + (x+2) + 18 = 0

 

[Drongoski]

I thought reducible to quadratic was something like (x+2)^2 + (x+2) + 18 = 0

precisely!

 

[Aquawhite]

I thought reducible to quadratic was something like (x+2)^2 + (x+2) + 18 = 0

Well the OP must have thought that would be the way to solve the question. Except it isn't quite the way of a reducible quadratic.... close

 

[vaaan]

Actually; it was what the exercise was called in my textbook ?