What is the answer to ((x+1)/x)^2=5 ?

The answer to ((x+1)/x)^2=5 is x=-(-1+sqrt(5))/4 ,x=(1+sqrt(5))/4

Solve for x: ((x+1)/x)^2=5

The solution is x=-(-1+sqrt(5))/4 ,x=(1+sqrt(5))/4

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(\frac{x + 1}{x})^{2} = 5

x = - \frac{- 1 + 5}{4}, x = \frac{1 + 5}{4}

Decimal Notation

x = - 0.30901 \dots, x = 0.80901 \dots

Solution steps

(\frac{x + 1}{x})^{2} = 5

Simplify

(\frac{x + 1}{x})^{2} : \frac{( x + 1 ) ^{2}}{x ^{2}}

\frac{( x + 1 ) ^{2}}{x ^{2}} = 5

Multiply both sides by

x^{2}

(x + 1)^{2} = 5 x^{2}

Solve

(x + 1)^{2} = 5 x^{2} : x = - \frac{- 1 + 5}{4}, x = \frac{1 + 5}{4}

x = - \frac{- 1 + 5}{4}, x = \frac{1 + 5}{4}

Verify Solutions

Find undefined (singularity) points:

x = 0

Combine undefined points with solutions:

x = - \frac{- 1 + 5}{4}, x = \frac{1 + 5}{4}

\frac{( 4 x )}{( 3 \cdot 4 \cdot 1 0 ^{4} - x )} = 4.45 \cdot 1 0^{- 7}

\frac{n !}{( n + 1 ) !} = 12

\frac{5 x ^{2} + 1}{x} = 6

\frac{( x ^{2} + 5 x + 6 )}{( x + 3 )} = x + 7

\frac{( x + 1 ) ^{2}}{( ( x + 2 ) ^{2} )} = \frac{( x + 2 )}{( x + 4 )}

What is the answer to ((x+1)/x)^2=5 ?
The answer to ((x+1)/x)^2=5 is x=-(-1+sqrt(5))/4 ,x=(1+sqrt(5))/4
Solve for x: ((x+1)/x)^2=5
The solution is x=-(-1+sqrt(5))/4 ,x=(1+sqrt(5))/4