TMUA Official Specimen Paper 2 · Question 3

Consider the following attempt to solve an equation. The steps have been numbered for reference.

\begin{gathered} \sqrt{x+5}=x+3\\ \Downarrow\quad\text{(1)}\\ x+5=x^2+6x+9\\ \Downarrow\quad\text{(2)}\\ x^2+5x+4=0\\ \Downarrow\quad\text{(3)}\\ (x+4)(x+1)=0\\ x=-4\text{ or }x=-1 \end{gathered}

Which one of the following statements is true?

ABoth

-4

and

-1

are solutions of the equation.

BNeither

-4

nor

-1

are solutions of the equation.

COne solution is correct and the incorrect solution arises as a result of step (1).

DOne solution is correct and the incorrect solution arises as a result of step (2).

EOne solution is correct and the incorrect solution arises as a result of step (3).

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