Which of the following is the reduced form of the equation $(2 x - 1)^{2} = x^{2} + 2$ ?

$4 x^{2} + 2 x + 1 = 0$

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${4 x}^{2} + 2 x - 1 = 0$

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${3 x}^{2} - 4 x - 1 = 0$

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${3 x}^{2} - 4 x + 1 = 0$

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Solution

The correct option is C
${3 x}^{2} - 4 x - 1 = 0$

Reduced form of an equation means make it into the standard form.

Given, $(2 x - 1)^{2} = x^{2} + 2$

$\Rightarrow 4 x^{2} - 4 x + 1 = x^{2} + 2$

$\Rightarrow 3 x^{2} - 4 x - 1 = 0$

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