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

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

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

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

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

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Solution

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

$(2 x - 1)^{2}$ = 4 $x^{2}$ + 1 - 4x

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

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

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

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