Solve by Factoring 1/pi=pi/16

$\frac{1}{π} = \frac{π}{16}$

Step 1

Subtract $\frac{π}{16}$ from both sides of the equation.

$\frac{1}{π} - \frac{π}{16} = 0$

Step 2

To write $\frac{1}{π}$ as a fraction with a common denominator, multiply by $\frac{16}{16}$ .

$\frac{1}{π} \cdot \frac{16}{16} - \frac{π}{16} = 0$

Step 3

To write $- \frac{π}{16}$ as a fraction with a common denominator, multiply by $\frac{π}{π}$ .

$\frac{1}{π} \cdot \frac{16}{16} - \frac{π}{16} \cdot \frac{π}{π} = 0$

Step 4

Write each expression with a common denominator of $π \cdot 16$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{1}{π}$ by $\frac{16}{16}$ .

$\frac{16}{π \cdot 16} - \frac{π}{16} \cdot \frac{π}{π} = 0$

Multiply $\frac{π}{16}$ by $\frac{π}{π}$ .

$\frac{16}{π \cdot 16} - \frac{π π}{16 π} = 0$

Reorder the factors of $π \cdot 16$ .

$\frac{16}{16 π} - \frac{π π}{16 π} = 0$

Step 5

Combine the numerators over the common denominator.

$\frac{16 - π π}{16 π} = 0$

Step 6

Simplify the numerator.

Multiply $- π π$ .

Raise $π$ to the power of $1$ .

$\frac{16 - (π π)}{16 π} = 0$

Raise $π$ to the power of $1$ .

$\frac{16 - (π π)}{16 π} = 0$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\frac{16 - π^{1 + 1}}{16 π} = 0$

Add $1$ and $1$ .

$\frac{16 - π^{2}}{16 π} = 0$

Rewrite $16 - π^{2}$ in a factored form.

Rewrite $16$ as $4^{2}$ .

$\frac{4^{2} - π^{2}}{16 π} = 0$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 4$ and $b = π$ .

$\frac{(4 + π) (4 - π)}{16 π} = 0$

Step 7

Set the numerator equal to zero.

$(4 + π) (4 - π) = 0$

Step 8

Solve the equation for .

Simplify $(4 + 3.14159265) (4 - (3.14159265))$ .

Remove parentheses.

$(4 + 3.14159265) (4 - (3.14159265)) = 0$

Add $4$ and $3.14159265$ .

$7.14159265 (4 - (3.14159265)) = 0$

Multiply $- 1$ by $3.14159265$ .

$7.14159265 (4 - 3.14159265) = 0$

Subtract $3.14159265$ from $4$ .

$7.14159265 \cdot 0.85840734 = 0$

Multiply $7.14159265$ by $0.85840734$ .

$6.13039559 = 0$

Since $6.13039559 \neq 0$ , there are no solutions.

No solution

Solve by Factoring 1/pi=pi/16

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