Respuesta :
Therefore the roots are, [tex]x=\frac{5+\sqrt{5}}{2},\:x=\frac{5-\sqrt{5}}{2}[/tex]
We have given that,
The two values of x that are the roots of this equation,
x² - 5x+ 5 = 0
What is the quadratic formula?
[tex]\mathrm{For\:a\:quadratic\:equation\:of\:the\:form\:}ax^2+bx+c=0\mathrm{\:the\:solutions\:are\:}[/tex]
[tex]\quad x_{1,\:2}=\frac{-b\pm \sqrt{b^2-4ac}}{2a}[/tex]
[tex]\mathrm{For\:}\quad a=1,\:b=-5,\:c=5[/tex]
[tex]x_{1,\:2}=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:1\cdot \:5}}{2\cdot \:1}[/tex]
[tex]x_{1,\:2}=\frac{-\left(-5\right)\pm \sqrt{\left(-5\right)^2-4\cdot \:1\cdot \:5}}{2\cdot \:1}[/tex]
[tex]x_{1,\:2}=\frac{-\left(-5\right)\pm \sqrt{5}}{2\cdot \:1}[/tex]
[tex]x_1=\frac{-\left(-5\right)+\sqrt{5}}{2\cdot \:1},\:x_2=\frac{-\left(-5\right)-\sqrt{5}}{2\cdot \:1}[/tex]
Therefore the roots are,
[tex]x=\frac{5+\sqrt{5}}{2},\:x=\frac{5-\sqrt{5}}{2}[/tex]
To learn more about the roots visit:
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