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What numbers add up to 5 and multiply up to -180 ?

Sagot :

konrad509
[tex]x+y=5\\ xy=-180\\\\ x=5-y\\ xy=-180\\\\ (5-y)y=-180\\ 5y-y^2+180=0\\ -y^2+5y+180=0\\ \Delta=5^2-4\cdot(-1)\cdot180=25+720=745\\ \sqrt{\Delta}=\sqrt{745}\\ y_1=\dfrac{-5-\sqrt{745}}{2\cdot(-1)}=\dfrac{5+\sqrt{745}}{2}\\ y_2=\dfrac{-5+\sqrt{745}}{2\cdot(-1)}=\dfrac{5-\sqrt{745}}{2}\\\\ x_1=5-\dfrac{5+\sqrt{745}}{2}=\dfrac{10}{2}-\dfrac{5+\sqrt{745}}{2}=\dfrac{5-\sqrt{745}}{2}\\ x_2=5-\dfrac{5-\sqrt{745}}{2}=\dfrac{10}{2}-\dfrac{5-\sqrt{745}}{2}=\dfrac{5+\sqrt{745}}{2}[/tex]

These numbers are [tex]\dfrac{5+\sqrt{745}}{2}[/tex] and [tex]\dfrac{5-\sqrt{745}}{2}[/tex].
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