Solve F(x)=-(x)^(2)YG(x)=(x)^(2)-3 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$F(x)=- { x }^{ 2 } YG(x)= { x }^{ 2 } -3$$

Solve for G (complex solution)

$\left\{\begin{matrix}G=\frac{3-x^{2}}{Yx^{3}}\text{, }&x\neq 0\text{ and }Y\neq 0\\G\in \mathrm{C}\text{, }&\left(x=\sqrt{3}\text{ or }x=-\sqrt{3}\right)\text{ and }Y=0\end{matrix}\right.$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add $2$ and $1$ to get $3$.

$$-x^{3}YG=x^{2}-3$$

The equation is in standard form.

$$\left(-Yx^{3}\right)G=x^{2}-3$$

Divide both sides by $-x^{3}Y$.

$$\frac{\left(-Yx^{3}\right)G}{-Yx^{3}}=\frac{x^{2}-3}{-Yx^{3}}$$

Dividing by $-x^{3}Y$ undoes the multiplication by $-x^{3}Y$.

$$G=\frac{x^{2}-3}{-Yx^{3}}$$

Divide $-3+x^{2}$ by $-x^{3}Y$.

$$G=-\frac{x^{2}-3}{Yx^{3}}$$

Solve for Y (complex solution)

$\left\{\begin{matrix}Y=\frac{3-x^{2}}{Gx^{3}}\text{, }&x\neq 0\text{ and }G\neq 0\\Y\in \mathrm{C}\text{, }&\left(x=\sqrt{3}\text{ or }x=-\sqrt{3}\right)\text{ and }G=0\end{matrix}\right.$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add $2$ and $1$ to get $3$.

$$-x^{3}YG=x^{2}-3$$

The equation is in standard form.

$$\left(-Gx^{3}\right)Y=x^{2}-3$$

Divide both sides by $-x^{3}G$.

$$\frac{\left(-Gx^{3}\right)Y}{-Gx^{3}}=\frac{x^{2}-3}{-Gx^{3}}$$

Dividing by $-x^{3}G$ undoes the multiplication by $-x^{3}G$.

$$Y=\frac{x^{2}-3}{-Gx^{3}}$$

Divide $-3+x^{2}$ by $-x^{3}G$.

$$Y=-\frac{x^{2}-3}{Gx^{3}}$$

Solve for G

$\left\{\begin{matrix}G=\frac{3-x^{2}}{Yx^{3}}\text{, }&x\neq 0\text{ and }Y\neq 0\\G\in \mathrm{R}\text{, }&Y=0\text{ and }|x|=\sqrt{3}\end{matrix}\right.$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add $2$ and $1$ to get $3$.

$$-x^{3}YG=x^{2}-3$$

The equation is in standard form.

$$\left(-Yx^{3}\right)G=x^{2}-3$$

Divide both sides by $-x^{3}Y$.

$$\frac{\left(-Yx^{3}\right)G}{-Yx^{3}}=\frac{x^{2}-3}{-Yx^{3}}$$

Dividing by $-x^{3}Y$ undoes the multiplication by $-x^{3}Y$.

$$G=\frac{x^{2}-3}{-Yx^{3}}$$

Divide $x^{2}-3$ by $-x^{3}Y$.

$$G=-\frac{x^{2}-3}{Yx^{3}}$$

Solve for Y

$\left\{\begin{matrix}Y=\frac{3-x^{2}}{Gx^{3}}\text{, }&x\neq 0\text{ and }G\neq 0\\Y\in \mathrm{R}\text{, }&G=0\text{ and }|x|=\sqrt{3}\end{matrix}\right.$

Steps for Solving Linear Equation

To multiply powers of the same base, add their exponents. Add $2$ and $1$ to get $3$.

$$-x^{3}YG=x^{2}-3$$

The equation is in standard form.

$$\left(-Gx^{3}\right)Y=x^{2}-3$$

Divide both sides by $-x^{3}G$.

$$\frac{\left(-Gx^{3}\right)Y}{-Gx^{3}}=\frac{x^{2}-3}{-Gx^{3}}$$

Dividing by $-x^{3}G$ undoes the multiplication by $-x^{3}G$.

$$Y=\frac{x^{2}-3}{-Gx^{3}}$$

Divide $x^{2}-3$ by $-x^{3}G$.

$$Y=-\frac{x^{2}-3}{Gx^{3}}$$