Question

решите уравнение 15x-x^2=25

Answer 1

15x-x²=25
-x²+15x-25=0
x²-15x+25=0
D=(-15)²-4*1*25=225-100=125
$\sqrt{D} = \sqrt{125}= \sqrt{25*5}=5 \sqrt{5} \\ x_1= \frac{-(-15)- \sqrt{125} }{2*1} = \frac{15-5 \sqrt{5}}{2} = \frac{5(3- \sqrt{5})}{2} =2,5(3- \sqrt{5}) \\ x_2= \frac{-(-15)+ \sqrt{125} }{2*1} = \frac{15+5 \sqrt{5}}{2} = \frac{5(3+ \sqrt{5})}{2} =2,5(3+ \sqrt{5})$