Answer:
A
Explanation:
STEP 1:
Isolate the square root on the left hand side
Radical already isolated
√2x-9 = x-6
STEP 2:
Eliminate the radical on the left hand side
Raise both sides to the second power
(√2x-9)2 = (x-6)2
After squaring
2x-9 = x2-12x+36
STEP 3:
Solve the quadratic equation
Rearranged equation
x2 - 14x + 45 = 0
This equation has two rational roots:
{x1, x2}={9, 5}
STEP 4:
Check that the first solution is correct
Original equation
√2x-9 = x-6
Plug in 9 for x
√2•(9)-9 = (9)-6
Simplify
√9 = 3
Solution checks !!
Solution is:
x = 9
STEP 5:
Check that the second solution is correct
Original equation
√2x-9 = x-6
Plug in 5 for x
√2•(5)-9 = (5)-6
Simplify
√1 = -1
Solution does not check
1 ≠ -1
One solution was found :
x=9
Hope this helps!!