Question

x^2-(x-0.1*x)^2=19. Rez ecuația

Answer 1

$x^2-(x-0.1x)^2=19 \\ x^2-(x- \frac{1}{10} x)^2=19 \\ x^2-[x^2-2 \cdot x \cdot \frac{1}{10} x+( \frac{1}{10} x)^2=19 \\ x^2-(x^2- \frac{2}{10} x^2+ \frac{1}{100} x^2)=19 \\ x^2-x^2+ \frac{2}{10}x^2- \frac{1}{100} x^2=19 \\ \frac{2}{10} x^2- \frac{1}{100} x^2=19 \\ 2x^2 \cdot 10-x^2=19 \cdot 100 \\ 20x^2-x^2=1900 \\ 19x^2=1900 \\ x^2=1900:19 \\ x^2=100 \\ x= \sqrt{100} \Rightarrow x=10~;~x=- \sqrt{100} \Rightarrow x=-10 \\ S=\{-10;10\}$