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x^2-101x+1=0
a = 1; b = -101; c = +1;
Δ = b2-4ac
Δ = -1012-4·1·1
Δ = 10197
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10197}=\sqrt{9*1133}=\sqrt{9}*\sqrt{1133}=3\sqrt{1133}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-101)-3\sqrt{1133}}{2*1}=\frac{101-3\sqrt{1133}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-101)+3\sqrt{1133}}{2*1}=\frac{101+3\sqrt{1133}}{2} $
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