Question

If x+1/16x=1 find 64x^3+1/64x^3

Answer 1

$x + \frac{1}{16x} = 1 \\ multiplying \: by \:4 \\ 4x + \frac{1}{4x} = 4 \\ by \: cubing \: the \: the \: equation \: we \: have \\ 64 { x}^{3} + \frac{1}{64 {x}^{3} } + 3(4x)( \frac{1}{4x} )(4x + \frac{1}{4x} ) \\ = 64 \\ 64 {x}^{3} + \frac{1}{64 {x}^{3} } + 3(4) = 64 \\ 64 {x}^{3} + \frac{1}{64 {x}^{3} } = 52$

Answer 2

Answer: The value of $64x^3+\dfrac{1}{64x^3}=52$

Step-by-step explanation:

Since we have given that

$x+\dfrac{1}{16x}=1$

We need to find the value of $64x^3+\dfrac{1}{64x^3}$

First we multiply the given expression by 4.

So, it becomes,

$4x+\dfrac{1}{4x}=4$

On Cubing both sides, we get that

$(4x+\dfrac{1}{4x})^3=4^3\\\\(4x)^3+(\dfrac{1}{4x})^3+3\times 4x\times \dfrac{1}{4x}(4x+\dfrac{1}{4x})=64\\\\64x^3+\dfrac{1}{64x^3}+3\times 4=64\\\\64x^3+\dfrac{1}{64x^3}=64-12=52$

Hence, the value of $64x^3+\dfrac{1}{64x^3}=52$