Question

What is the solution to the equation square root 2x + 6 - square root x + 4 = 1

Answer 1

raAnswer:

x = 5

Step-by-step explanation:

Original equation = $\sqrt{2x+6}$ - $\sqrt{x+4}$ = 1

Remove square roots

$x^{2}$ + 2x +1 = 4x +16

Subtract 16 from both sides

$x^{2}$+ 2x +1 = 4x +16

           -16       -16

---------------------------

$x^{2}$  + 2x- 15= 4x

Subtract 4x from both sides

$x^{2}$ + 2x - 15 - 4x= 4x - 4x

= $x^{2}$ - 2x - 15 = 0

THIS EQUATION HAS 2 rational roots. {x1,x2} = {5,-3}

CHECK THAT THE FIRST SOLUTION IS CORRECT (5)

    Original equation, root isolated, after tidy up

  $\sqrt{2x+6}$ = $\sqrt{x+4}$

     Plug in 5 for  x

$\sqrt{2\cdot (5)+6}$ = $\sqrt{(5)+4+1}$

        Simplify

      $\sqrt16}$ = 4

  Solution checks !!

     Solution is: x = 5

CHECK THAT THE SECOND SOLUTION IS CORRECT (-3)

 Original equation, root isolated, after tidy up

  $\sqrt{2x+6}$ = $\sqrt{x+4}$

   Plug in  -3 for  x

  $\sqrt{2\cdot (-3) +6}$ = $\sqrt{(-3)+4+1}$

       Simplify

$\sqrt{0}$ = 2

 Solution does not check

          0 ≠ 2

   So, the answer is x = 5

Hope this helps!