Quy đồng :

\(x=\frac{-22}{55};y=\frac{-15}{55}\)

Vậy \(x< y\)

~HT~

\(C=\frac{y^2-1}{y^2}\left(ĐK:y\ne0\right)\)

Ta có: \(C>0\Rightarrow\frac{y^2-1}{y^2}>0\)

Mà \(y^2>0\Rightarrow y^2-1>0\Rightarrow y^2>1\Rightarrow\orbr{\begin{cases}y< -1\\y>1\end{cases}}\)

Đề C có giá trị dương thì:

       \(\frac{y^2-1}{y^2}>0\left(y\in Q^+\right)\) ( Vì \(y^2\ge0;y\ne0\)

\(\rightarrow y^2-1\ge0\)

 Nhưng vì C lờn hơn 0 nên:

\(\rightarrow y^2-1>0\rightarrow y^2>1\rightarrow\orbr{\begin{cases}y>1\\y< -1\end{cases}}\)

Ta có :

\(\frac{x+2}{11}+\frac{x+2}{12}+\frac{x+2}{13}=\frac{x+2}{14}+\frac{x+2}{15}\)

\(\Rightarrow\frac{x+2}{11}+\frac{x+2}{12}+\frac{x+2}{13}-\frac{x+2}{14}-\frac{x+2}{15}=0\)

\(\Rightarrow\left(x+2\right).\left(\frac{1}{11}+\frac{1}{12}+\frac{1}{13}-\frac{1}{14}-\frac{1}{15}\right)=0\)

\(\Rightarrow x+2=0\left(\text{do }\frac{1}{11}+\frac{1}{12}+\frac{1}{13}-\frac{1}{14}-\frac{1}{15}\ne0\right)\)

\(\Rightarrow x=-2\)

\(2^{225}=\left(2^3\right)^{75}=8^{75}\)

\(3^{150}=\left(3^2\right)^{75}=9^{75}\)

\(8^{75}< 9^{75}\Rightarrow2^{225}< 3^{150}\)

Bài 2 ; 2 ; 3 ; 4 phần tự luận bạn tham khảo ở Câu hỏi của Phùng minh long - Toán lớp 7 - Học trực tuyến OLM nhé !

Bài 1 :

\(1)\frac{11}{24}-\frac{5}{41}+\frac{13}{24}+0,5-\frac{36}{41}\)

\(\Rightarrow\left(\frac{11}{24}+\frac{13}{24}\right)-\left(\frac{5}{41}+\frac{36}{41}\right)+\frac{1}{2}\)

\(\Rightarrow1-1+\frac{1}{2}=\frac{1}{2}\)

\(2)\frac{15}{34}+\frac{7}{21}+\frac{19}{34}-1\frac{15}{17}+\frac{2}{3}\)

\(=\frac{15}{34}+\frac{7}{21}+\frac{19}{34}-1-\frac{15}{17}+\frac{14}{21}\)

\(=\left(\frac{15}{34}+\frac{19}{34}-1\right)+\left(\frac{7}{21}+\frac{14}{21}\right)-\frac{15}{17}\)

\(=1-\frac{15}{17}=\frac{2}{17}\)

\(3)1\frac{4}{23}+\frac{5}{21}-\frac{4}{23}+0,5+\frac{16}{21}\)

\(=\left(1\frac{4}{23}-\frac{4}{23}\right)+\left(\frac{5}{21}+\frac{16}{21}\right)+0,5\)

\(=1+1+0,5=2,5\)

\(4)\left(-12\right):\left(\frac{3}{4}-\frac{5}{6}\right)^2\)

\(=\left(-12\right):\left(\frac{-1}{12}\right)^2\)

\(=\left(-12\right).12^2=-12^3\)

\(5)\left(\frac{9}{25}-2.18\right):\left(3\frac{4}{5}+0,2\right)\)

\(=\frac{-891}{25}:4=\frac{-891}{100}\)

\(6)\left(-6,5\right).5,7+5,7.\left(-3,5\right)\)

\(=\left[\left(-6,5\right)+\left(-3,5\right)\right].5,7\)

\(=-10.5,7=57\)

\(7)-3,75.\left(-7,2\right)+2,8.3,75\)

\(=3,75.7,2+2,8.3,75\)

\(=3,75.\left(7,2+2,8\right)\)

\(=3,75.10=37,5\)

\(8)23\frac{1}{4}.\frac{7}{5}-13\frac{1}{4}:\frac{5}{7}\)

\(=23\frac{1}{4}.\frac{7}{5}-13\frac{1}{4}.\frac{7}{5}\)

\(=\left(23\frac{1}{4}-13\frac{1}{4}\right).1,4\)

\(=10.1,4=14\)

\(9)16\frac{2}{7}:\left(\frac{-3}{5}\right)+28\frac{2}{7}:\frac{3}{5}\)

\(=-16\frac{2}{7}:\frac{3}{5}+28\frac{2}{7}:\frac{3}{5}\)

\(=-16\frac{2}{7}.\frac{5}{3}+28\frac{2}{7}.\frac{5}{3}\)

\(=\left(-16\frac{2}{7}+28\frac{2}{7}\right).\frac{5}{3}\)

\(=12.\frac{5}{3}=20\)

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