# Solve the equation (x+8)^1/2 + (x-2)^1/2 = 5

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To solve (x+8)^(1/2)+(x-2)^1/2 = 5

Solution:

Squaring both sides of the given equation, we get:

(x+8)+2[(x+8)(x-2)]^(1/2)+x-2=25. OR rearranging,

2[(x+8)(x-2)]^(1/2) = 25-(x+8)-(x-2) =-(2x-19). Or

2[(x+8)(x-2)]^(1/2) =(19-2x). Squaring qgain both sides,

4(x+8)(x-2) = (2x-19)^2. Or

4x^2+24x-64 = 4x^2-76x+361 Or

24x+76x = 361+64 = 425 Or

100x = 4.25/100 = 4.25.

(x+8)^1/2 + (x-2)^1/2 = 5

Let's multiply, to both sides of the identity, with the adjoint expression of (x+8)^1/2 + (x-2)^1/2.

[(x+8)^1/2 + (x-2)^1/2][(x+8)^1/2 - (x-2)^1/2]=5[(x+8)^1/2 - (x-2)^1/2]

To the left side, we'll have:

[(x+8)^1/2]^2 - [(x-2)^1/2]^2=x+8-x+2=10

The identity will become:

10 = 5[(x+8)^1/2 - (x-2)^1/2]

2 = [(x+8)^1/2 - (x-2)^1/2]

Let's sum up this result with the initial equation

(x+8)^1/2 + (x-2)^1/2 + (x+8)^1/2 - (x-2)^1/2 = 2+5

2(x+8)^1/2 = 7

(x+8)^1/2 = 7/2

(x+8) = 49/4

x = 49/4 - 8

x = (49-32)/4

**x=17/4**

Now, we'll verify the result, by putting into equation:

(17/4 + 8)^1/2 + (17/4 - 2)^1/2 = 5

[(17+32)^1/2]/2 + [(17-8)^1/2]/2 = 5

7/2 + 3/2 = 5

10/2 = 5

5=5, true!

That means that x=17/4 is the solution of the equation.

5

(x+8)^1/2 + (x-2)^1/2 = 5 Computed by Wolfram|Alpha Your Input Plot5