Question

Ştiind că 5a+4b/5a+7b = 2/3, calculati b^2-a^2/2a^2 - 3ab + b^2

Answer 1

[tex]\frac{5a+4b}{5a+7b}=\frac{2}{3}\Rightarrow 15a+12b=10a+14b\\ ~~~~~~~~~~~~~~~~~~~5a=2b\Rightarrow \frac{a}{b}=\frac{2}{5}\Rightarrow \frac{a}{2}=\frac{b}{5}=k\Rightarrow a=2k;b=5k\\ Ca\ fapt\ divers:2a^2-3ab+b^2=2a^2-2ab-ab+b^2=\\ =2a(a-b)-b(a-b)=(a-b)(2a-b)\\ Si\ b^2-a^2=(b-a)(a+b)(probabil\ stiai\ asta)\\ Revenind:\\ \frac{b^2-a^2}{2a^2-3ab+b^2}=\frac{(b-a)(b+a)}{(a-b)(2a-b)}=\frac{b+a}{b-2a}=\frac{2k+5k}{5k-2k}=\frac{7k}{3k}=\boxed{\frac{7}{3}}[/tex]