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

Question

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

Team Careers360 · Accepted Answer

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, $(x+1)^{3}+\frac{1}{(x+1)^{3}}=2^3-3 imes 2$
$= 8 – 6 = 2$
Hence, the correct answer is 2.

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Question : If x+5+1x+1=6, then the value of (x+1)3+1(x+1)3 is:Option 1: 2Option 2: 0Option 3: –2Option 4: 4

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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