Question

Roots of equation x^2-2root2x+1=0

Answer 1

Step-by-step explanation:

${x}^{2} - 2 \sqrt{2}x + 1 = 0 \\ compare \: equation \: with \: a {x}^{2} + bx + c = 0 \\ a = 1 \: \: \: \: b = - 2 \sqrt{2} \: \: \: \: \: c = 1 \\ {b}^{2} - 4ac = {( - 2 \sqrt{2}) }^{2} - 4 \times 1 \times 1 \\ = 4 \times 2 - 4 \\ = 8 - 4 \\ = 4 \\ using \: formula \\ x = \frac{ - b + - \sqrt{ {b}^{2} - 4ac } }{2a} \\ x = \frac{ - ( - 2 \sqrt{2}) + - \sqrt{4} }{2} \\ x = \frac{ 2 \sqrt{2} + 4}{2} \: \: \: \: or \: \: \: x = \frac{2 \sqrt{2} - 4 }{2} \\ x = \frac{2( \sqrt{2} + 2) }{2} \: \: \: or \: \: \: x = \frac{2( \sqrt{2} - 2) }{2} \\ x = \sqrt{2} + 2 \: \: \: \: \: or \: x = \sqrt{2} - 2$

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