# Solve: x^3 - y = In y; (1, 1)

## Question:

Solve:

{eq}x^3 - y = In y; (1, 1) {/eq}

## Simplifying criteria:

To simplify any mathematical expression is converting from one equal form to another such that the second form is less complex to the first one.

Following some rule which we used in the given example:

{eq}a + b = c\,\, \Rightarrow a = c - b {/eq}

## Answer and Explanation:

Given that: {eq}\displaystyle {x^3} - y = \ln y {/eq}

{eq}\displaystyle \eqalign{ & {x^3} - y = \ln y \cr & {x^3} = \ln y + y \cr & x = \root 3 \of {y + \ln y} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {{\text{For real solution}}} \right) \cr & \cr & x = \root 3 \of {1 + \ln 1} \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {y(1) = 1} \right) \cr & x = \root 3 \of {1 + 0} \cr & x = 1 \cr & \cr & x = \root 3 \of {y + \ln y} \cr} {/eq}

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