Question

$$\left. \begin{array} { l l } { | c | c | c | c | } y = \frac { 1 } { 3 } x ^ { 2 } } \\ x & { - 6 | - 3 | 0 & { 3 } \\ y & { 12 } & { 0 } & { 3 } \\ \end{array} \right.$$

Answer

$$x=1/41^(1/263036),-1/41^(1/263036)$$

Solution


Use this rule: \(\frac{a}{b} \times \frac{c}{d}=\frac{ac}{bd}\).
\[y=\frac{1\times {x}^{263036}y\times 123}{3}\]
Simplify  \(1\times {x}^{263036}y\times 123\)  to  \(123{x}^{263036}y\).
\[y=\frac{123{x}^{263036}y}{3}\]
Simplify  \(\frac{123{x}^{263036}y}{3}\)  to  \(41{x}^{263036}y\).
\[y=41{x}^{263036}y\]
Divide both sides by \(41\).
\[\frac{y}{41}={x}^{263036}y\]
Divide both sides by \(y\).
\[\frac{\frac{y}{41}}{y}={x}^{263036}\]
Simplify  \(\frac{\frac{y}{41}}{y}\)  to  \(\frac{y}{41y}\).
\[\frac{y}{41y}={x}^{263036}\]
Cancel \(y\).
\[\frac{1}{41}={x}^{263036}\]
Take the \(263036\)th root of both sides.
\[\pm \sqrt[263036]{\frac{1}{41}}=x\]
Use Division Distributive Property: \({(\frac{x}{y})}^{a}=\frac{{x}^{a}}{{y}^{a}}\).
\[\pm \frac{1}{\sqrt[263036]{41}}=x\]
Switch sides.
\[x=\pm \frac{1}{\sqrt[263036]{41}}\]

Decimal Form: ±0.999986