Question

ajutoor ex 17 ofer coroana si 50 de puncte!!

Answer 1

a)
 [tex]\frac{x}{1.2}=\frac{(2.5-1\frac{2}{3})^2}{\frac{5}{24}}\\ \\ \frac{x}{\frac{12}{10}}=\frac{(\frac{25}{10}-\frac{5}{3})^2}{\frac{5}{24}}\\ [/tex]
Aducem la acelasi numitor, acesta fiind 30
[tex]\frac{10}{12}x=\left(\frac{3\cdot25-10\cdot5}{30}\right)^2\cdot\frac{24}{5}\\ \\ \frac{10}{12}x=\left(\frac{75-50}{30}\right)^2\cdot\frac{24}{5}\\ \\ \frac{10}{12}x=\frac{25^2}{30^2}\cdot\frac{24}{5}\\ \\ \frac{10}{12}x=\frac{625}{900}\cdot\frac{24}{5}[/tex]
Simplificam 900 si 24 prin 4, si 625 si 5 prin 5:
[tex]\frac{10}{12}x=\frac{125\cdot6}{225}\\ \\ 10x\cdot225=12\cdot125\cdot6\\ \\ 2250x=9000\\ \\ x=\frac{9000}{2250}=4[/tex]
b)
[tex]\frac{8\frac{8}{15}\left[\frac{1}{5}+x\left(1\frac{1}{3}-1\frac{1}{5}\right)\right]\cdot1\frac{2}{3}}{2,1(3)}=\frac{16^8}{8^{10}}=\frac{2^8\cdot8^8}{8^8\cdot8^2}=\frac{2^3\cdot2^3\cdot2^2}{8^2}=2^2\\ \\ \frac{\frac{128}{15}\left[\frac{1}{5}+x\left(\frac{4}{3}-\frac{6}{5}\right)\right]\cdot\frac{5}{3}}{\frac{213-21}{90}}=4\\ \\ \frac{128}{15}\cdot(\frac{1}{5}+\frac{20-18}{15}x)\cdot\frac{5}{3}\cdot\frac{90}{192}=4\\ \\ \frac{128\cdot5\cdot90}{15\cdot3\cdot192}\cdot\frac{3+2}{15}x=4\\[/tex]
[tex]\frac{57600}{8640}\cdot\frac{5}{15}x=4\\ [/tex]
Prin simplificari:
[tex]\frac{20}{3}\cdot\frac{5}{15}x=4\\ \\ 100x=4\cdot45\\ x=\frac{180}{100}=1,8[/tex]