Asked by Louise
Solve the equation
(the square root of x+2)+ (the square root of x-2)=(the square root of 4x-2)
(the square root of x+2)+ (the square root of x-2)=(the square root of 4x-2)
Answers
Answered by
Reiny
√(x+2) + √(x-2) = √(4x-2)
square both sides
[√(x+2) + √(x-2)]^2 = [√(4x-2)]^2
x+2 + 2√(x^2 - 4) + x-2 = 4x - 2
2√(x^2 - 4) = 2x - 2
√(x^2 - 4) = x-1
square again
x^2 - 4 = x^2 - 2x + 1
2x = 5
x = 5/2 or 2.5
since we squared, we must check the answer in the original equation, it does work.
square both sides
[√(x+2) + √(x-2)]^2 = [√(4x-2)]^2
x+2 + 2√(x^2 - 4) + x-2 = 4x - 2
2√(x^2 - 4) = 2x - 2
√(x^2 - 4) = x-1
square again
x^2 - 4 = x^2 - 2x + 1
2x = 5
x = 5/2 or 2.5
since we squared, we must check the answer in the original equation, it does work.
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.