Решите уравнение : 1600 ( 1 - x/100)^2 = 1156 Должно получиться 15

[latex]1600(1-\frac{x}{100})^{2} =1156 \\ (1-\frac{x}{100})^{2} = \frac{1156}{1600} \\ (1-\frac{x}{100})^{2} =0,7225 \\ 1- \frac{2x}{100}+ \frac{ x^{2} }{10000}=0,7225[/latex] [latex]\frac{10000-200x+ x^{2} }{10000} =0,7225 \\ x^{2} -200x+10000=7225 \\ x^{2} -200x+2775=0 \\ D=40000-4*2775=170^{2} \\ x1= \frac{200+170}{2} =185 \\ x2= \frac{200-170}{2} =15[/latex]Ответ: 185; 15

[latex]1600=40^2; 1156=34^2[/latex] [latex](40(1- \frac{x}{100} ))^2=34^2[/latex] [latex](40- \frac{2x}{5})^2-34^2=0 [/latex] [latex](40- \frac{2x}{5}+34)(40- \frac{2x}{5}-34)=0 [/latex] [latex]( \frac{370-2x}{5})( \frac{30-2x}{5})=0 [/latex] [latex]370-2x=0; x_1=185[/latex] [latex]30-2x=0; x_2=15[/latex]