Ta có

\(\frac{4^{n+3}+17.2^{2n}}{9^{n+1}+7.3^{2n}}=\frac{2^{2n+6}+17.2^{2n}}{3^{2n+2}+7.3^{2n}}=\frac{2^{2n}.\left(2^6+17\right)}{3^{2n}.\left(3^2+7\right)}=\left(\frac{2}{3}\right)^{2n}.\frac{81}{16}=1\)

\(\Rightarrow\left(\frac{2}{3}\right)^{2n}.\frac{3^4}{2^4}=1\Rightarrow\left(\frac{2}{3}\right)^{2n}=\left(\frac{2}{3}\right)^4\Rightarrow2n=4\Rightarrow n=2\)

Ta có : \(C^k_{2n+1}=C^{2n+1-k}_{2n+1}\)

\(\Rightarrow2VT=C^1_{2n+1}+C^2_{2n+1}+...+C^{2n}_{2n+1}=2^{21}-2\)

\(\Leftrightarrow2^{2n+1}-C^0_{2n+1}-C^{2n+1}_{2n+1}=2^{21}-2\)

\(\Leftrightarrow2n+1=21\Leftrightarrow n=10\)

\(\sum\limits^{2n+1}_{k=0}C^k_{2n+1}=\left(1+1\right)^{2n+1}=2^{2n+1}\)

Lại có \(C^0_{2n+1}+C^1_{2n+1}+...+C^n_{2n+1}=C^{2n+1}_{2n+1}+C^{2n}_{2n+1}+...+C^{n+1}_{2n+1}\)

\(\Rightarrow C^0_{2n+1}+C^1_{2n+1}+...C^n_{2n+1}=\dfrac{2^{2n+1}}{2}\)

\(\Leftrightarrow2^{20}-1=2^{2n}-C^0_{2n+1}\)

\(\Leftrightarrow2^{20}-1=2^{2n}-1\)

\(\Leftrightarrow2n=20\)

\(\Leftrightarrow n=10\)

Thay n = 4 vào pt (1) ta có

\(x^2-6x+5=0\\ ta.có.a+b+c=1-6+5=0\\ Vậy.pt.có.n_o:\\ x_1=1;x_2=\dfrac{c}{a}=5\) 

\(Ta.có:\Delta=b^2-4ac=....=-8n+48\\ Để.pt.\left(1\right).có.1.n_o.phân.biệt.thì.\Delta>0\\ \Leftrightarrow n< 6\) 

Vậy m < 6 thì pt (1) có nghiệm phân biệt \(x_1;x_2\) nên theo Vi ét ta có 

 \(x_1+x_2=\dfrac{-b}{a}=6\\ x_1x_2=\dfrac{c}{a}=2n-3\) 

Ta có  

\(x^2-6x+2n-3=0\\ \Leftrightarrow x^2-5x+2n-4=x-1\) 

Vì x₁ x₂ là nghiệm pt  \(x^2-6x+2n-3=0\) nên x₁ x₂ là nghiệm PT \(x^2-5x+2n-4=x-1\)  nên ta có 

\(x_1^2-5x+2x-4=x_1-1.và\\ x_2^2-5x_2+2n-4=x_2-1\\ \Rightarrow\left(x_1^2-5x_1+2n-4\right)\left(x_2^2-5x_2+2n-4\right)=\left(x_1-1\right)\left(x_2-1\right)\) 

\(Mà\\ \left(x_1^2-5x_1+2n-4\right)\left(x_2^2-5x_2+2n-4\right)=-4\\ Nên\left(x_1-1\right)\left(x_2-1\right)=-4\\ \Leftrightarrow x_1x_2-\left(x_1+x_2\right)+1=-4\\ \Leftrightarrow2n-3-6+1=-4\\ \Leftrightarrow2n=4\Rightarrow n=2\left(tm\right)\\ ......\left(kl\right)\) 

ý a bạn bt lm ko?

không ạ mình hỏi các bạn bài này ạ!

ĐÂY LÀ BÀI TÌM X TƯƠNG TỰ PHẢI KHÔNG

2N-4=6

2N=6+4

2N=10

N=10/2

N=5

2n-4=6

2n=6+4

2n=10

n=10:2

n=5

2n - 4 = 6 

2n      = 6 + 4 

2n      = 10

 n       = 10 : 2 

 n       = 5

Vậy n = 5