\(\frac{1}{9}\cdot3^4\cdot3^n=3^7\)

\(\frac{1}{9}\cdot3^n=3^7:3^4\)

\(\frac{1}{9}\cdot3^n=3^3\)

\(\frac{1}{9}\cdot3^n=27\)

\(3^n=27:\frac{1}{9}\)

\(3^n=243\)

\(3^n=3^5\)

=> \(n=5\)

\(\frac{1}{9}.3^4.3^n=3^7\\ \frac{1}{9}.81.3^n=3^7\\ 9.3^n=3^7\\ 3^2.3^n=3^7\\ 3^{n+2}=3^7\\ n+2=7\\ n=5\)

TA CÓ:

\(\sqrt{x-1-4\sqrt{x-1}+4}+\sqrt{x-1+6\sqrt{x-1}+9}=5\)

\(\Leftrightarrow\sqrt{\left(\sqrt{x-1}-2\right)^2}+\sqrt{\left(\sqrt{x-1}-3\right)^2}=5\)

\(\Leftrightarrow\sqrt{x-1}-2+\sqrt{x-1}-3=5\Leftrightarrow2\sqrt{x-1}=10\Leftrightarrow\sqrt{x-1}=5\)

\(\Leftrightarrow x-1=25\Leftrightarrow x=26\)

ĐKXĐ: \(x\ge1\)

PT (=) \(\sqrt{\left(\sqrt{x-1}-2\right)^2}+\sqrt{\left(\sqrt{x-1}+3\right)^2}=5\) 

     (=) \(\sqrt{x-1}-2+\sqrt{x-1}+3=5\) (=)  \(2\sqrt{x-1}=4\)(=) \(\sqrt{x-1}=2\)(=) X = 5 (nhận)

Ta có: \(x^4-30x^2+31x-30=0\) \(\Rightarrow x^4+x-30x^2+30x-30=0\)

\(\Rightarrow x\left(x^3+1\right)-30\left(x^2-x+1\right)=0\)

\(\Rightarrow x\left(x+1\right)\left(x^2-x+1\right)-30\left(x^2-x+1\right)=0\)

\(\Rightarrow\left(x^2-x+1\right)\left(x^2+x-30\right)=0\)

Xét \(x^2-x+1=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}\ge\frac{3}{4}>0\)

\(\Rightarrow x^2+x-30=0\Rightarrow x^2-5x+6x-30=0\)

\(\Rightarrow\left(x-5\right)\left(x+6\right)=0\Rightarrow\orbr{\begin{cases}x-5=0\\x+6=0\end{cases}\Rightarrow\orbr{\begin{cases}x=5\\x=-6\end{cases}}}\)

Vậy x=5 hoặc x = -6

\(x^3-2x^2-2x+3=0\)

\(\Leftrightarrow x^3-x^2-x^2+x-3x+3=0\)

\(\Leftrightarrow x^2\left(x-1\right)-x\left(x-1\right)-3\left(x-1\right)=0\)

\(\Leftrightarrow\left(x^2-x-3\right)\left(x-1\right)=0\)

...

Có số số hạng là : 

(x - 10) + 1 = x - 9 (số hạng)

Tổng trên là :

(x + 10) . (x - 9) : 2 = 5106

=> (x + 10) . (x - 9) = 10212

=> (x + 10) . (x - 9) = 111 . 92

=> (x + 10) . (x - 9) = (101 + 10) . (101 - 9)

=> 101

 minh nha 

làm ơn giải đi mà,ai giải ra mình mang ơn suốt đời

\(3x=4y\Leftrightarrow\frac{x}{4}=\frac{y}{3}\)

Áp dụng t/c dãy tỉ số bằng nhau, ta có:

\(\frac{x}{4}=\frac{y}{3}=\frac{x+y}{4+3}=\frac{56}{7}=8\)

\(\Rightarrow\hept{\begin{cases}x=8.4=32\\y=8.3=24\end{cases}}\)

Vậy x = 32; y = 24

TL:

Ta có:\(3x=4y\Rightarrow\frac{x}{4}=\frac{y}{3}\) 

Áp dụng.........

\(\frac{x}{4}=\frac{y}{3}=\frac{x+y}{4+3}=\frac{56}{12}=\frac{14}{3}\) 

=>x=\(\frac{56}{3}\) ;\(y=14\) 

vậy.......

hc tốt