Solve A-(1)/(A)=0TOA+(1)/(A) | 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

$$A- \frac{ 1 }{ A } =0TOA+ \frac{ 1 }{ A }$$

Solve for A

$A=\sqrt{2}\approx 1.414213562$
$A=-\sqrt{2}\approx -1.414213562$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Variable $A$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $A$.

$$AA-1=0TOAA+1$$

Multiply $A$ and $A$ to get $A^{2}$.

$$A^{2}-1=0TOAA+1$$

Multiply $A$ and $A$ to get $A^{2}$.

$$A^{2}-1=0TOA^{2}+1$$

Anything times zero gives zero.

$$A^{2}-1=0+1$$

Add $0$ and $1$ to get $1$.

$$A^{2}-1=1$$

Add $1$ to both sides.

$$A^{2}=1+1$$

Add $1$ and $1$ to get $2$.

$$A^{2}=2$$

Take the square root of both sides of the equation.

$$A=\sqrt{2}$$ $$A=-\sqrt{2}$$

Steps Using the Quadratic Formula

Variable $A$ cannot be equal to $0$ since division by zero is not defined. Multiply both sides of the equation by $A$.

$$AA-1=0TOAA+1$$

Multiply $A$ and $A$ to get $A^{2}$.

$$A^{2}-1=0TOAA+1$$

Multiply $A$ and $A$ to get $A^{2}$.

$$A^{2}-1=0TOA^{2}+1$$

Anything times zero gives zero.

$$A^{2}-1=0+1$$

Add $0$ and $1$ to get $1$.

$$A^{2}-1=1$$

Subtract $1$ from both sides.

$$A^{2}-1-1=0$$

Subtract $1$ from $-1$ to get $-2$.

$$A^{2}-2=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $1$ for $a$, $0$ for $b$, and $-2$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$A=\frac{0±\sqrt{0^{2}-4\left(-2\right)}}{2}$$

Square $0$.

$$A=\frac{0±\sqrt{-4\left(-2\right)}}{2}$$

Multiply $-4$ times $-2$.

$$A=\frac{0±\sqrt{8}}{2}$$

Take the square root of $8$.

$$A=\frac{0±2\sqrt{2}}{2}$$

Now solve the equation $A=\frac{0±2\sqrt{2}}{2}$ when $±$ is plus.

$$A=\sqrt{2}$$

Now solve the equation $A=\frac{0±2\sqrt{2}}{2}$ when $±$ is minus.

$$A=-\sqrt{2}$$

The equation is now solved.

$$A=\sqrt{2}$$ $$A=-\sqrt{2}$$

Solve for O (complex solution)

$O\in \mathrm{C}$
$A=-\sqrt{2}\text{ or }A=\sqrt{2}$

Solve for O

$O\in \mathrm{R}$
$|A|=\sqrt{2}$