What are the solutions to the equation X^2-4X+1=0 ?

The solutions to the equation X^2-4X+1=0 are X=2+sqrt(3),X=2-sqrt(3)

Find the zeros of X^2-4X+1=0

The zeros of X^2-4X+1=0 are X=2+sqrt(3),X=2-sqrt(3)

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X^{2} - 4 X + 1 = 0

X = 2 + 3, X = 2 - 3

Decimal Notation

X = 3.73205 \dots, X = 0.26794 \dots

Solution steps

X^{2} - 4 X + 1 = 0

Solve with the quadratic formula

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

(- 4)^{2} - 4 \cdot 1 \cdot 1 = 23

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

Separate the solutions

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

X = \frac{- ( - 4 ) + 2 3}{2 \cdot 1} : 2 + 3

X = \frac{- ( - 4 ) - 2 3}{2 \cdot 1} : 2 - 3

The solutions to the quadratic equation are:

X = 2 + 3, X = 2 - 3

2 x^{2} + 12 x - 10 = 0

x, g = p (x - q)^{2} + r - 3

x^{2} - 242 = 0

- 6 x^{2} + 36 x - 84 = 0

x, f (x + 2) = 4 x^{2} + 5

What are the solutions to the equation X^2-4X+1=0 ?
The solutions to the equation X^2-4X+1=0 are X=2+sqrt(3),X=2-sqrt(3)
Find the zeros of X^2-4X+1=0
The zeros of X^2-4X+1=0 are X=2+sqrt(3),X=2-sqrt(3)