Question

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

Answer 1

$1600(1-\frac{x}{100})^{2} =1156 \\ (1-\frac{x}{100})^{2} = \frac{1156}{1600} \\ (1-\frac{x}{100})^{2} =0,7225 \\ 1- \frac{2x}{100}+ \frac{ x^{2} }{10000}=0,7225$

$\frac{10000-200x+ x^{2} }{10000} =0,7225 \\ x^{2} -200x+10000=7225 \\ x^{2} -200x+2775=0 \\ D=40000-4*2775=170^{2} \\ x1= \frac{200+170}{2} =185 \\ x2= \frac{200-170}{2} =15$ответ: 185; 15

Answer 2

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