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

Answer: (D)

Both A and B

Answer 2

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.