If $$m + \frac{1}{{m - 2}} = 4{\text{,}}$$ find the value of $${\left( {m - 2} \right)^2}{\text{ + }}\frac{1}{{{{\left( {m - 2} \right)}^2}}}$$ is?
A. -2
B. 0
C. 2
D. 4
Answer: Option C
Solution(By Examveda Team)
$$\eqalign{ & m + \frac{1}{{m - 2}} = 4 \cr & \Rightarrow m - 2 + \frac{1}{{m - 2}} = 2 \cr & \left( {{\text{Squaring the both sides}}} \right) \cr} $$$$ \Rightarrow {\left( {m - 2} \right)^2}{\text{ + }}\frac{1}{{{{\left( {m - 2} \right)}^2}}} + 2 \times $$ $$\left( {m - 2} \right) \times $$ $$\frac{1}{{\left( {m - 2} \right)}}$$ $$ = 4$$
$$ \Rightarrow {\left( {m - 2} \right)^2}{\text{ + }}\frac{1}{{{{\left( {m - 2} \right)}^2}}} = 2$$
Related Questions on Algebra
If $$p \times q = p + q + \frac{p}{q}{\text{,}}$$ then the value of 8 × 2 is?
A. 6
B. 10
C. 14
D. 16
A. $$1 + \frac{1}{{x + 4}}$$
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C. $$\frac{1}{x}$$
D. $$\frac{{x + 4}}{x}$$
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B. $$\frac{{27}}{{20}}$$
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D. $$\frac{8}{6}$$
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