What is the answer to x/((1+x)^{0.5)}=1 ?

The answer to x/((1+x)^{0.5)}=1 is x=(1+5^{1/2})/2

Solve for x: x/((1+x)^{0.5)}=1

The solution is x=(1+5^{1/2})/2

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\frac{x}{( 1 + x ) ^{0.5}} = 1

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

Decimal Notation

x = 1.61803 \dots

Solution steps

\frac{x}{( 1 + x ) ^{0.5}} = 1

Multiply both sides by

(1 + x)^{0.5}

\frac{x}{( 1 + x ) ^{0.5}} (1 + x)^{0.5} = 1 \cdot (1 + x)^{0.5}

Simplify

x = (1 + x)^{0.5}

Square both sides:

x^{2} = 1 + x

x^{2} = 1 + x

Solve

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

x = \frac{1 + 5 ^{\frac{1}{2}}}{2}, x = \frac{1 - 5 ^{\frac{1}{2}}}{2}

Verify Solutions:

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

True

, x = \frac{1 - 5 ^{\frac{1}{2}}}{2}

False

The solution is

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

3 x - 1 + 1 = 7

80 = 4 (30 - q)

3 x + 2 = 6 x - 1

\frac{1}{2 x} - 1 = 0

(2 x - 1)^{2} = 3

What is the answer to x/((1+x)^{0.5)}=1 ?
The answer to x/((1+x)^{0.5)}=1 is x=(1+5^{1/2})/2
Solve for x: x/((1+x)^{0.5)}=1
The solution is x=(1+5^{1/2})/2