√x + 1 + √2x - 5 = 3
Answers
Step-by-step explanation:
Step by step solution :Step 1 :Isolate a square root on the left hand side :
Original equation
√x+1+√2x-5 = 3
Isolate
√x+1 = -√2x-5+3
Step 2 :Eliminate the radical on the left hand side :
Raise both sides to the second power
(√x+1)2 = (-√2x-5+3)2
After squaring
x+1 = 2x-5+9-6√2x-5
Step 3 :Get remaining radical by itself :
Current equation
x+1 = 2x-5+9-6√2x-5
Isolate radical on the left hand side
6√2x-5 = -x-1+2x-5+9
Tidy up
6√2x-5 = x+3
Step 4 :Eliminate the radical on the left hand side :
Raise both sides to the second power
(6√2x-5)2 = (x+3)2
After squaring
72x-180 = x2+6x+9
Step 5 :Solve the quadratic equation :
Rearranged equation
x2 - 66x + 189 = 0
This equation has two rational roots:
{x1, x2}={63, 3}
Step 6 :Check that the first solution is correct :
Original equation, root isolated, after tidy up
√x+1 = -√2x-5+3
Plug in 63 for x
√(63)+1 = -√2•(63)-5+3
Simplify
√64 = -8
Solution does not check
8 ≠ -8
Step 7 :Check that the second solution is correct :
Original equation, root isolated, after tidy up
√x+1 = -√2x-5+3
Plug in 3 for x
√(3)+1 = -√2•(3)-5+3
Simplify
√4 = 2
Solution checks !