Question

If \((4x^2+\frac{1}{4x^2})=2\), then what is the value of \((8x^3+\frac{1}{8x^3})\) ?
A) +2
B) -2
C) +4
D) -4

• A. Only A
• B. Only C
• C. Both C and D
• D. Both A and B

Answer 1

The Correct Option is D

As we know, (a + b)2 = a2 + b2 + 2ab
Then, \((2x+\frac{1}{2x})^2=(4x^2+\frac{1}{4x^2}+2(2x(\frac{1}{2x}))\)
\((2x+\frac{1}{2x})^2=2+2=4\)
\((2x+\frac{1}{2x})=±2\)
Similarly, we know, (a + b)3 = a3 + b3 + 3ab(a + b)
Now, \((2x+\frac{1}{2x})^3=(8x^3+\frac{1}{8x^3}+3(2x)(\frac{1}{2x})(2x+\frac{1}{2x}))\)
\((±2)^3=8x^3+\frac{1}{8x^3}+3\times(±2)\)
\(8x^3+\frac{1}{8x^3}=±2\)
So, the correct option is (D) : Both A and B.