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

Question

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

Team Careers360 · Accepted Answer

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+1a−2=4, then the value of (a−2)2+(1a−2)2 is:Option 1: 0Option 2: 2Option 3: –2Option 4: 4

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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