Solve the following equation:
$(x - 2)^{2} = (x + 1) (x - 1)$

1.5

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1.75

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2.25

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1.25

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Solution

The correct option is D $1.25$
Given, $(x - 2)^{2} = (x + 1) (x - 1)$
$\Rightarrow x^{2} - 4 x + 4 = x^{2} - 1$ .... Using $(a - b) (a + b) = a^{2} - b^{2}$
$\Rightarrow - 4 x + 4 = - 1$
$\Rightarrow - 4 x = - 5$
$\Rightarrow x = \frac{5}{4} = 1.25$

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