To solve √x+5=x-1, a student squares to get x=4 or x=-1 and reports both. What is correct?

Worked solution for TMUA-P2-ERR2-015 is revealed on this page behind the solution details.

Why isn't the answer to TMUA-P2-ERR2-015 shown upfront?

The options are lettered without marking the correct one so you attempt TMUA-P2-ERR2-015 first — TMUA questions reward spotting the trap before you check the worked solution below.

Do I need a calculator for TMUA-P2-ERR2-015?

No — calculators are banned in the TMUA. TMUA-P2-ERR2-015 is set for a no-calculator target of about 180 seconds; the worked solution shows the fastest by-hand route.

Which TMUA specification point is TMUA-P2-ERR2-015?

TMUA-P2-ERR2-015 is Paper P2 · Common fallacies (specification code ERR2), level 2. Drill more of the same topic from this page.

TMUA-P2-ERR2-015 — Paper P2 · Common fallacies · Level 2

P2ERR2Level 2~180s target

Spec: ERR2 · No calculator · ~180s

To solve

\sqrt{x+5}=x-1

, a student squares to get

x=4

x=-1

and reports both. What is correct?

Options

Both $x=4$ and $x=-1$ are valid.
Only $x=4$ ; $x=-1$ gives $\sqrt{4}=2 \ne -2$ and violates $x-1 \ge 0$ , so squaring introduced an extraneous root.
Only $x=-1$ .
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: extraneous-root-squaring, domain-check-omission. Name the trap first, work the stem by hand, then open the solution below.

Show solution

Squaring is not reversible without

x-1 \ge 0

and

x+5 \ge 0

. Here

x=4

checks (

3=3

) but

x=-1

fails (

2 \ne -2

). Trap: accepting every root of the squared equation without substituting back.

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Browse more

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Options

Both

x=4

and

x=-1

are valid.

Only

x=4

;

x=-1

gives

\sqrt{4}=2 \ne -2

and violates

x-1 \ge 0

, so squaring introduced an extraneous root.

Only

x=-1

There are no real solutions.

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

Keep practising

Same topic · same level

P2ERR2Level 2

TMUA-P2-ERR2-004

A student solves -2x > 6 by dividing both sides by -2 to get x > -3. What is the error?

Common fallacies

Open TMUA-P2-ERR2-004 →

Step up a 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 →

TMUA-P2-ERR2-015 — Paper P2 · Common fallacies · Level 2

Options

Keep practising

Master Common fallacies

TMUA-P2-ERR2-015 — Paper P2 · Common fallacies · Level 2

Options

Keep practising

Master Common fallacies