TMUA 2018 Paper 2 Q9 — Worked Solution

P2·Algebra & Surds, Logic & Quantifiers·6.5Official · 2018 · Q9

radical-equationlost-rootdividing-by-zero-factor

Consider the following attempt to solve the equation

4 x 2 x - 1 = 10 x - 5

(I)

4 x 2 x - 1 = 5 (2 x - 1)

(II)

16 x^{2} (2 x - 1) = 25 (2 x - 1)^{2}

(III)

16 x^{2} = 25 (2 x - 1)

(IV)

16 x^{2} - 50 x + 25 = 0

(V)

(8 x - 5) (2 x - 5) = 0

(VI)

The solutions of the original equation are

x = \frac{5}{8}

and

x = \frac{5}{2}

Which one of the following is true?

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