Question : If $x+5+\frac{1}{x+1}=6$, then the value of $(x+1)^{3}+\frac{1}{(x+1)^{3}}$ is:
Option 1: 2
Option 2: 0
Option 3: –2
Option 4: 4
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Answer (1)
25th Jan, 2024
Correct Answer: 2
Solution :
Given: $x+5+\frac{1}{x+1}=6$
Subtracting both sides 4
$x+1+\frac{1}{x+1}=2$
Use formula,
$a^3+b^3 = (a+b)^3-3ab(a+b)$
So, $(x+1)^{3}+\frac{1}{(x+1)^{3}}=2^3-3\times 2$
$= 8 – 6 = 2$
Hence, the correct answer is 2.
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