x (x 1) 1 = 0 ⇒ x^2 x 1 = 0 x= 1 + √( 1 (4× 1× 1) ) #160; 2× 1 =1 + √( 1+4 ) 2 x_1 = 1+√(5)/2 x_2 = 1 √(5)/2 ...

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Quadratic Formula

Solve; xx-1...

Question

Solve; $x (x - 1) = 1$

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Solution

$x (x - 1) - 1 = 0$

$\Rightarrow x^{2} - x - 1 = 0$

$x = \frac{1 \begin{matrix} + - \end{matrix} \sqrt{1 - (4 \times 1 \times - 1)}}{2 \times 1} = \frac{1 \begin{matrix} + - \end{matrix} \sqrt{1 + 4}}{2}$

$x_{1} = \frac{1 + \sqrt{5}}{2} x_{2} = \frac{1 - \sqrt{5}}{2}$

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