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01 / Standard#Your turn

x^2-3x+4\sqrt{x^2-3x}=12

Official paper · jm01-2023 · I.4 · PDF 2

Skills and prerequisite lessons

Working and explanation

BUILD THE REASONING

Hint 1

Set t=√(x²−3x), with t≥0.

Hint 2

Solve for t before returning to x.

Worked solution

Factor the equation in t.
$t^2+4t-12=(t-2)(t+6)=0\implies t=2$
Solve the remaining quadratic and check its radicand.
$x^2-3x=4\iff(x-4)(x+1)=0$

C: {−1,4}.

Checks and common pitfalls: Reject t=−6 because t is a principal square root.

Reasoning checklist · self / teacher assessment

Teaching assessment checklist, independently authored. Use the original paper for official marks.
Factor the equation in t.
$t^2+4t-12=(t-2)(t+6)=0\implies t=2$
Solve the remaining quadratic and check its radicand.
$x^2-3x=4\iff(x-4)(x+1)=0$

Think first. Reveal a hint when the class is ready.

2023 JM01