Solve a - 1/a = 0; a + 1/a तो | 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

$$a - \frac { 1 } { a } = 0 a + \frac { 1 } { a }$$

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 $a$.

$$aa-1=0aa+1$$

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

$$a^{2}-1=0aa+1$$

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

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

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 $a$.

$$aa-1=0aa+1$$

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

$$a^{2}-1=0aa+1$$

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

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

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.

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