Question : If $a+\frac{1}{a-2}=4$, then the value of $(a-2)^{2}+(\frac{1}{a-2})^{2}$ is:
Option 1: 0
Option 2: 2
Option 3: –2
Option 4: 4
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Correct Answer: 2
Solution : Given: $a+\frac{1}{a-2}=4$ Subtracting 2 from both sides, ⇒ $a-2+\frac{1}{a-2}=2$ Squaring both sides, ⇒ $( a-2)^2+\frac{1}{( a-2)^2} + 2=2^2$ ⇒ $( a-2)^2+\frac{1}{( a-2)^2}=2^2-2$ ⇒ $( a-2)^2+\frac{1}{( a-2)^2}=2$ Hence, the correct answer is 2.
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Question : If $(a+\frac{1}{a})=–2$, then the value of $a^{1000}+a^{–1000}$ is:
Question : If $a+\frac{1}{a}=1$, then the value of $\frac{a^2-a+1}{a^2+a+1}$ is $(a\neq 0)$:
Question : If $(x+\frac{1}{x})^{2}=3$, then the value of $(x^{3}+\frac{1}{x^{3}})$ is:
Question : If $\frac{3–5x}{2x}+\frac{3–5y}{2y}+\frac{3–5z}{2z}=0$, the value of $\frac{2}{x}+\frac{2}{y}+\frac{2}{z}$ is:
Question : If $\frac{a}{b}+\frac{b}{a}=1$, then the value of $(a^3+b^3)$ is:
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