Question

Sa-mi explice cineva (nu doar sa rezolve) cum holy snitel se rezolva dracovenia asta:
$\frac{1}{100} x^{2} -\frac{1}{64}=0$

Answer 1

 

$\displaystyle\bf\\\frac{1}{100}x^2-\frac{1}{64}=0\\\\\\\frac{x^2}{100}-\frac{1}{64}=0\\\\\\\frac{x^2}{10^2}-\frac{1}{8^2}=0\\\\\\\left(\frac{x}{10}\right)^{\b2}-\left(\frac{1}{8}\right)^{\b2}=0$

.

$\displaystyle\bf\\Folosim~formula:~~~a^2-b^2=(a-b)(a+b)\\\\\left(\frac{x}{10}-\frac{1}{8}\right)\left(\frac{x}{10}+\frac{1}{8}\right)=0\\\\\\\frac{x}{10}-\frac{1}{8}=0~\implies~\frac{x}{10}=\frac{1}{8}~\implies~x_1=\frac{10}{8}~\implies~\boxed{\bf~x_1=\frac{5}{4}}\\\\\\\frac{x}{10}+\frac{1}{8}=0~\implies~\frac{x}{10}=-\frac{1}{8}~\implies~x_2=-\frac{10}{8}~\implies~\boxed{\bf~x_2=-\frac{5}{4}}$