The student's error is not checking the solutions by keeping the values in problem equation. The correct solution is 4.
Rewriting the equation to find the solution of expression -
√x+2=x
Shifting 2 to Right Hand Side of the equation
√x = x - 2
Taking square on both sides
(√x)² = (x - 2)²
Solving the bracket on both sides of the equation -
x = x² - 4x + 4
Solving the equation for the value of x by factorizing it
x² - 4x - x + 4 = 0
x² - 5x + 4 = 0
x² - 4x - x + 4 = 0
x(x - 4) -1(x - 4) = 0
(x - 4) (x - 1) = 0
x = 4, 1
Keep the value of x to validate the result and find correct solution -
x = 1
√x+2=x
√1 + 2 = 1
1 + 2 = 1
3 ≠ 1
x = 4
√4+2=4
2 + 2 = 4
4 = 4
Hence, the correct solution is 4.
Learn more about factorization of solution -
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The complete question is -
A student said that 4 and 1 are the solutions of the problem shown. Describe and correct the student's error. √x+2=x
