16Hit 1600
Advanced MathVery hardSubstitution for a radical quadratic

Advanced Math practice question

If x − √x = 6 and x > 0, what is the value of x?

Answer: 9

Let t = √x: t² − t − 6 = 0 factors as (t − 3)(t + 2) = 0. Only t = 3 is allowed, so x = t² = 9.

Common wrong answers

If you answered 3
3 is √x; the question asks for x = 9.
If you answered 4
Check: 4 − 2 = 2 ≠ 6.
If you answered 36
36 − 6 = 30 ≠ 6; solve the t-quadratic first.

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