TMUA Official 2018 Paper 2 · Question 9

Consider the following attempt to solve the equation $4x\sqrt{2x-1}=10x-5$ :

\begin{gathered} 4x\sqrt{2x-1}=10x-5\\[2pt] \underset{\text{(I)}}{\Downarrow}\\[2pt] 4x\sqrt{2x-1}=5(2x-1)\\[2pt] \underset{\text{(II)}}{\Downarrow}\\[2pt] 16x^2(2x-1)=25(2x-1)^2\\[2pt] \underset{\text{(III)}}{\Downarrow}\\[2pt] 16x^2=25(2x-1)\\[2pt] \underset{\text{(IV)}}{\Downarrow}\\[2pt] 16x^2-50x+25=0\\[2pt] \underset{\text{(V)}}{\Downarrow}\\[2pt] (8x-5)(2x-5)=0\\[2pt] \underset{\text{(VI)}}{\Downarrow} \end{gathered}

The solutions of the original equation are $x=\frac58$ and $x=\frac52$ .

Which one of the following is true?

AThe solution is correct.

BOnly one of

x=\frac58

and

x=\frac52

is correct and the error arises as a result of step (II).

COnly one of

x=\frac58

and

x=\frac52

is correct and the error arises as a result of step (III).

DOnly one of

x=\frac58

and

x=\frac52

is correct and the error arises as a result of step (IV).

EThere is another value of

x

that satisfies the original equation and the error arises as a result of step (II).

FThere is another value of

x

that satisfies the original equation and the error arises as a result of step (III).

GThere is another value of

x

that satisfies the original equation and the error arises as a result of step (IV).

examday