√(x + 3)+√(x - 3)=6, solve x (please solve it in step by step and please don't spam)
Answers
Answer:
STEP: 1
:
Isolate a square root on the left hand side
Original equation
√x+3+√x-3 = 6
Isolate
√x+3 = -√x-3+6
STEP 2
:
Eliminate the radical on the left hand side
Raise both sides to the second power
(√x+3)2 = (-√x-3+6)2
After squaring
x+3 = x-3+36-12√x-3
STEP 3
:
Get remaining radical by itself
Current equation
x+3 = x-3+36-12√x-3
Isolate radical on the left hand side
12√x-3 = -x-3+x-3+36
Tidy up
12√x-3 = 30
STEP 4
:
Eliminate the radical on the left hand side
Raise both sides to the second power
(12√x-3)2 = (30)2
After squaring
144x-432 = 900
STEP 5
:
Solve the linear equation
Rearranged equation
144x -1332 = 0
Add 1332 to both sides
144x = 1332
Divide both sides by 144
A possible solution is :
x = (37/4)
STEP 6
:
Check that the solution is correct
Original equation, root isolated, after tidy up
√x+3 = -√x-3+6
Plug in (37/4) for x
√(37/4)+3 = -√(37/4)-3+6
Simplify
√12.25 = 3.5
Solution checks !!
Solution is:
x = (37/4)
One solution was found :
x = (37/4)