Question

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

Answer 1

raAnswer:

x = 5

Explanation:

Original equation =
`√(2x+6)` -
`√(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

`√(2x+6)` =
`√(x+4)`

Plug in 5 for x

`√(2\cdot (5)+6)` =
`√((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

`√(2x+6)` =
`√(x+4)`

Plug in -3 for x

`√(2\cdot (-3) +6)` =
`√((-3)+4+1)`

Simplify

`√(0)` = 2

Solution does not check

0 ≠ 2

So, the answer is x = 5

Hope this helps!