Question

0,(1)$x^{2}$-0,25=($\frac{x}{3}$-2)$^{2}$

Answer 1

Daca paranteza din dreapta este inmultita cu 2, ecuatia nu are solutii, asa ca cred ca ecuatia este asa:

$\dfrac{x^2}{9}-\dfrac14=(\dfrac x3-2)^2$

$\dfrac{x^2}{9}-\dfrac14=\dfrac{x^2}{9}-\dfrac{4x}{3}+4$

$\dfrac{4x}{3}=4+\dfrac14$

$\dfrac{4x}{3}=\dfrac{17}{4}$

$x=\dfrac{3\cdot17}{16}=\dfrac{51}{16}=3\dfrac{3}{16}$