Find the solution for the equation [(x + 7)^1/2] + [ x - 1)^1/2] = 4

Let's multiply the adjoint expression of the left side, to
the both sides of the equation.

{[(x+7)^1/2] +
[(x-1)^1/2]}X{[(x+7)^1/2] - [(x-1)^1/2]}= 4x{[(x+7)^1/2] -
[(x-1)^1/2]}

Multiplying the paranthesis from the left
side

[(x+7)^1/2]^2 - [(x+7)^1/2]x[(x-1)^1/2] +
[(x+7)^1/2]x[(x-1)^1/2] - [(x-1)^1/2]^2= 4x{[(x+7)^1/2] -
[(x-1)^1/2]}

(x+7) - (x-1) = 4x{[(x+7)^1/2] -
[(x-1)^1/2]}

Opening the paranthesis from the left
side

x + 7 -x +1= 4x{[(x+7)^1/2] -
[(x-1)^1/2]}

8 = 4x{[(x+7)^1/2] -
[(x-1)^1/2]}

• 2= {[(x+7)^1/2] -
  [(x-1)^1/2]}

Let's sum up this result with the
initial equation

[(x+7)^1/2] - [(x-1)^1/2] + [(x+7)^1/2] +
[(x-1)^1/2] = 6

One can note that two terms are the same:
[(x+7)^1/2] and the other two term are opposite: [(x-1)^1/2], the last ones being
reduced.

2x[(x+7)^1/2]=6

[(x+7)^1/2]=3

[(x+7)^1/2]^2=3^2

x+7=9

x=9-7

x=2

After
verifying action, we can conclude that x=2 is the solution of the
equation.