What are the solutions to the equation X^2-3X+1=0 ?

The solutions to the equation X^2-3X+1=0 are X=(3+sqrt(5))/2 ,X=(3-sqrt(5))/2

Find the zeros of X^2-3X+1=0

The zeros of X^2-3X+1=0 are X=(3+sqrt(5))/2 ,X=(3-sqrt(5))/2

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X^{2} - 3 X + 1 = 0

X = \frac{3 + 5}{2}, X = \frac{3 - 5}{2}

Decimal Notation

X = 2.61803 \dots, X = 0.38196 \dots

Solution steps

X^{2} - 3 X + 1 = 0

Solve with the quadratic formula

X_{1, 2} = \frac{- ( - 3 ) \pm ( - 3 ) ^{2} - 4 \cdot 1 \cdot 1}{2 \cdot 1}

(- 3)^{2} - 4 \cdot 1 \cdot 1 = 5

X_{1, 2} = \frac{- ( - 3 ) \pm 5}{2 \cdot 1}

Separate the solutions

X_{1} = \frac{- ( - 3 ) + 5}{2 \cdot 1}, X_{2} = \frac{- ( - 3 ) - 5}{2 \cdot 1}

X = \frac{- ( - 3 ) + 5}{2 \cdot 1} : \frac{3 + 5}{2}

X = \frac{- ( - 3 ) - 5}{2 \cdot 1} : \frac{3 - 5}{2}

The solutions to the quadratic equation are:

X = \frac{3 + 5}{2}, X = \frac{3 - 5}{2}

3 x^{2} - 3 x + 0.54 = 0

r^{2} - \frac{2}{3} r = 0

x^{2} = [0.0 8^{2} \cdot 0.7 3^{2}] + [0.0 2^{2} \cdot 5.1 4^{2}]

x^{2} + 33 x = 430

21980 = 0.68 \cdot 20 x \cdot (\frac{2.5}{1.4}) (45 - 0.4 x)

What are the solutions to the equation X^2-3X+1=0 ?
The solutions to the equation X^2-3X+1=0 are X=(3+sqrt(5))/2 ,X=(3-sqrt(5))/2
Find the zeros of X^2-3X+1=0
The zeros of X^2-3X+1=0 are X=(3+sqrt(5))/2 ,X=(3-sqrt(5))/2