Question

Se considera ecuatia x^2-2m+m=0, m real, iar x1,x2 radacinile reale ale ecuatiei.
Stim ca |x1-x2|=1, deci, m=?

Answer 1

$Poti~afla~radacinile:\\ \\ \Delta=4-4m=4(1-m)\\ \\ x_1=\frac{2-2\sqrt{1-m}}{2} \\ \\ x_2=\frac{2+2\sqrt{1-m}}{2} \\ \\ |\frac{2-2\sqrt{1-m}-2-2\sqrt{1-m}}{2} |=1\\ \\ |\frac{-4\sqrt{1-m}}{2} |=1\\ \\ 4\sqrt{1-m} =2\\ \\ \sqrt{1-m} =\frac{1}{2} \\ \\ m=\frac{3}{4}$

Answer 2

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