Why isn't the answer to TMUA-P2-ERR2-018 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P2-ERR2-018 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P2-ERR2-018?

No — calculators are banned in the TMUA. TMUA-P2-ERR2-018 is set for a no-calculator target of about 240 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P2-ERR2-018?

TMUA-P2-ERR2-018 is Paper P2 · Common fallacies (specification code ERR2), level 3. Drill more of the same topic from this page.

TMUA-P2-ERR2-018 — Paper P2 · Common fallacies · Level 3

P2ERR2Level 3~240s target

Spec: ERR2 · No calculator · ~240s

A student solves

(2x-1)^2=(x+2)^2

by taking square roots to get

2x-1=x+2

, hence

x=3

only. What is the full solution set?

Options

$x=3$ only.
$x=3$ or $x=-\tfrac13$ ; the case $2x-1=-(x+2)$ was dropped.
$x=-3$ only.
There are no real solutions.

Letters only — the answer key is hidden. Work it out, then check the solution below.

Hint (check trope)

No written hint yet — check the trope: sqrt-sign-drop, plus-minus-omission. Name the trap first, work the stem by hand, then open the solution below.

Show solution

A^2=B^2

means

A=\pm B

. The minus case gives

2x-1=-x-2

, i.e.

x=-\tfrac13

, which also satisfies the equation. Trap: taking roots with only the positive sign.

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Keep practising

Same topic · same level

P2ERR2Level 3

TMUA-P2-ERR2-009

A sixth-former optimises a profit function P(x) and argues as follows: Fermat's theorem says that if P has a local maxim…

Common fallacies

Open TMUA-P2-ERR2-009 →

Same trap: sqrt-sign-drop

P2ERR2Level 1

TMUA-P2-ERR2-012

Mia solves x^2=9 and concludes x=3. What is the error?

Common fallacies

Open TMUA-P2-ERR2-012 →

TMUA-P2-ERR2-018 — Paper P2 · Common fallacies · Level 3

Options

Keep practising

Master Common fallacies

TMUA-P2-ERR2-018 — Paper P2 · Common fallacies · Level 3

Options

Keep practising

Master Common fallacies