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Bài 4:
\(a,2^{30}=\left(2^3\right)^{10}=8^{10};3^{20}=\left(3^2\right)^{10}=9^{10}\\ Vì:8^{10}< 9^{10}\left(Vì:8< 9\right)\Rightarrow2^{30}< 3^{20}\\ b,9^{10}.27^5=\left(3^2\right)^{10}.\left(3^3\right)^5=3^{20}.3^{15}=3^{35}\\ 243^7=\left(3^5\right)^7=3^{35}\\ Vì:3^{35}=3^{35}\Rightarrow243^7=9^{10}.27^5\)
Tham khảo qua link đây nhé cậu :
https://books.google.com.vn/books?id=PhymDAAAQBAJ&pg=PA59&lpg=PA59&dq=T%C3%ACm+c%C3%A1c+s%E1%BB%91+nguy%C3%AAn+a,b,c+th%E1%BB%8Fa+m%C3%A3n+a%5E2%2Bab%3D5a%2B2b%2B9&source=bl&ots=8bzSP0h3kN&sig=ACfU3U2A_d9ME7r47hAsdMemtJWUaW1w_A&hl=vi&sa=X&ved=2ahUKEwjg89-r0_HoAhUkK6YKHWIXCnkQ6AEwAnoECAwQKw#v=onepage&q=T%C3%ACm%20c%C3%A1c%20s%E1%BB%91%20nguy%C3%AAn%20a%2Cb%2Cc%20th%E1%BB%8Fa%20m%C3%A3n%20a%5E2%2Bab%3D5a%2B2b%2B9&f=false
Học tốt
\(a^2 + ab = 5a + 2b + 9 \)
\(\Leftrightarrow a^2+ab-5a-2b+6=15\)
\(\Leftrightarrow a\left(a+b\right)-2\left(a+b\right)-3\left(a-2\right)=15\)
\(\Leftrightarrow\left(a-2\right)\left(a+b\right)-3\left(a-2\right)=15\)
\(\Leftrightarrow\left(a-2\right)\left(a+b-3\right)=15\)
Do \(a,b\in Z\Rightarrow\hept{\begin{cases}a-2\in Z\\a+b-3\in Z\end{cases}}\)
\(\Rightarrow\left(a-2\right);\left(a+b-3\right)\inƯ\left(15\right)=\left\{1;-1;3;-3;5;-5;15;-15\right\}\)
\(\left(+\right)\hept{\begin{cases}a-2=1\\a+b-3=15\end{cases}\Rightarrow}a=3;b=15\)
\(\left(+\right)\hept{\begin{cases}a-2=-1\\a+b-3=-15\end{cases}\Rightarrow}a=1;b=-13\)
\(\left(+\right)\hept{\begin{cases}a-2=3\\a+b-3=5\end{cases}\Rightarrow}a=5;b=3\)
\(\left(+\right)\hept{\begin{cases}a-2=-3\\a+b-3=-5\end{cases}}\Rightarrow a=-1;b=-1\)
\(\left(+\right)\hept{\begin{cases}a-2=15\\a+b-3=1\end{cases}\Rightarrow}a=17;b=-13\)
\(\left(+\right)\hept{\begin{cases}a-2=-15\\a+b-3=-1\end{cases}\Rightarrow}a=-13;b=15\)
\(\left(+\right)\hept{\begin{cases}a-2=5\\a+b-3=3\end{cases}\Rightarrow a=7;b=-1}\)
\(\left(+\right)\hept{\begin{cases}a-2=-5\\a+b-3=-3\end{cases}\Rightarrow}a=-3;b=3\)
Vậy \(\left(a,b\right)=\left(3,15\right);\left(1,-13\right);\left(5,3\right);\left(-1,-1\right);\left(17,-13\right);\left(-13,15\right);\left(7,-1\right);\left(-3,3\right)\)
a+3c +a+2b = 17
=>2a +2b +3c = 17
=>2.(a+b)+3c=17
=>a+b+3c/2=17/2
=> N= a+b-c-17/2=a+b-c-a-b -3c/2=-c-3c/2
=> N là các số không âm
6x - 14 / 13 = 5y + 9 / 11 => ( 6x - 14 ) . 11 = ( 5y + 9 ) . 13
=> 66x - 154 = 65y + 117
=> 66x - 65y = 154 + 117
=> 66x - 65y = 271
Ta có \(\frac{6x-14}{13}=\frac{5y+9}{11}\)
=> \(11\left(6x-14\right)=13\left(5y+9\right)\)
=> \(66x-154=65y+117\)
=> \(66x-65y=117+154\)
=> \(66x-65y=271\)(1)
và \(3x-2y=19\)(2)
Trừ (1) với (2), ta có:
\(63x-63y=252\)
=> \(63\left(x-y\right)=252\)
=> \(x-y=\frac{252}{63}\)
=> \(x-y=4\)
=> x = 4 + y (3)
Thế (3) vào (2), ta có:
\(3\left(4+y\right)-2y=19\)
=> \(12+3y-2y=19\)
=> \(12+y=19\)
=> \(y=7\)
=> \(x=4+7=11\)
Vậy \(\hept{\begin{cases}x=11\\y=7\end{cases}}\)thì thoả mãn điều kiện \(\hept{\begin{cases}\frac{6x-14}{13}=\frac{5y+9}{11}\\3x-2y=19\end{cases}}\).
giúp mình vs ak mình cần gấp ak