Question 27

If $$a+\frac{1}{a-2}=4$$, then the value of $$(a-2)^{2}+(\frac{1}{a-2})^{2}$$ is

Solution

$$a+\frac{1}{a-2}=4$$

subtract 2 on both sides,

$$(a-2)+\frac{1}{a-2}=4-2$$

$$(a-2)+\frac{1}{a-2}=2$$

squaring on both sides

$$[(a-2)+\frac{1}{a-2}]^{2}=4$$

$$(a-2)^{2}+(\frac{1}{a-2})^{2}+2(a-2).(\frac{1}{a-2})=4$$

$$(a-2)^{2}+(\frac{1}{a-2})^{2}+2=4$$

$$(a-2)^{2}+(\frac{1}{a-2})^{2}=4-2=2$$

so the answer is option B.

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