Radical(x+3) +Radical(x) = 5?

Question

Help if you please.

Answer 1

1) I assume you want to solve for x

2) First, square both sides
x + x +3 + 2 * sqrt(x(x+3)) = 25

3) Rearrange
sqrt(x(x+3)) = 11 - x

4) Square both sides again
x^2 + 3x = 121 + x^2 - 22x

5) Simplifying
25x = 121

6) Finally
x = 121 / 25

7) Verify
U = sqrt(x+3) + sqrt(x)
U = sqrt(121 / 25 + 75 / 25) + sqrt(121/25) = 14 / 5 + 11 / 5 = 25 / 5 = 5

Answer 2

To solve: Radical(x + 3) +Radical(x) = 5, take one of the radicals on the other side getting:

Radical(x + 3) = 5 - Radical(x). Now square both sides:

x + 3 = 25 + x - 10*Radical(x)

or subtracting x and simplifying, we get:

3 - 25 = - 10*Radical(x)

or

- 22 = -10*Radical(x). Dividing by the common -2 and squaring:

121 = 25*x. Hence x = 121/25 = 4.84 is the solution.

Answer 3

r(x+3)+r(x)=5
r(x+3) = 5-r(x) square both sides
x+3 = 25 -10r(x) +x
10r(x)=22
x=(11/5)^2= 4.84
good luck