(x-7)^x+1-(x-7)^x+11=0

=>x-7=0

=>x=7

(8x-1)²ⁿ⁺¹=5²ⁿ⁺¹

=>8x-1=5

=>8x=6

=>x=3/4

Tick Đúng Nha

sao lại C^3_2n+1 nhỉ

ta có \(\left(1+1\right)^{2n+1}=C_{2n+1}^0+C^1_{2n+1}+C^2_{2n+1}+...+C^{2n+1}_{2n+1}\)

\(-\left(1-1\right)^{2n+1}=-\left(C_{2n+1}^0-C^1_{2n+1}+C^2_{2n+1}-...-C^{2n+1}_{2n+1}\right)\)

\(\left(1+1\right)^{2n+1}-\left(1-1\right)^{2n+1}=C_{2n+1}^0+C^1_{2n+1}+C^2_{2n+1}+...+C^{2n+1}_{2n+1}-C_{2n+1}^0+C_{2n+1}^1-C_{2n+1}^2+....+C_{2n+1}^{2n+1}\)

\(2^{2n+1}=2C_{2n+1}^1+2C_{2n+1}^3+2C_{2n+1}^5+...+C_{2n+1}^{2n+1}=2.1024=2048\)

\(\Rightarrow n=5\)

\(\left(2-3x\right)^{10}\)

SHTQ \(C_{10}^k.2^{10-k}.\left(-3x\right)^k=C_{10}^k.2^{10-k}.-3^k.x^k\)

\(x^7\Rightarrow k=7\)

hệ số cần tìm \(C_{10}^7.2^3.\left(-3\right)^7=-2099520\)

1=(2n+1)C0, (2n+1)Cn=(2n+1)C(n+1)...

a) \(a\left(b+1\right)=3\left(a;b\inℤ\right)\)

\(\Rightarrow a;\left(b+1\right)\in U\left(3\right)=\left\{-1;1;-3;3\right\}\)

\(\Rightarrow\left(a;b\right)\in\left\{\left(-1;-4\right);\left(1;2\right);\left(-3;-2\right);\left(3;0\right)\right\}\)

b) \(2n+7⋮n+1\left(n\inℤ\right)\)

\(\Rightarrow2n+7-2\left(n+1\right)⋮n+1\)

\(\Rightarrow2n+7-2n-2⋮n+1\)

\(\Rightarrow5⋮n+1\)

\(\Rightarrow n+1\in U\left(5\right)=\left\{-1;1;-5;5\right\}\)

\(\Rightarrow n\in\left\{-2;0;-6;4\right\}\)

c) \(xy+x-y=6\left(x;y\inℤ\right)\)

\(\Rightarrow x\left(y+1\right)-y-1+1=6\)

\(\Rightarrow x\left(y+1\right)-\left(y+1\right)=5\)

\(\Rightarrow\left(x-1\right)\left(y+1\right)=5\)

\(\Rightarrow\left(x-1\right);\left(y+1\right)\in U\left(5\right)=\left\{-1;1;-5;5\right\}\)

\(\Rightarrow\left(x;y\right)\in\left\{\left(-0;-6\right);\left(2;4\right);\left(-4;-2\right);\left(6;0\right)\right\}\)