Câu hỏi của Anhhh Duc (Bốp)

Question

help mn ơi <...

phong nguyen · Accepted Answer

xét phân số thứ nhất:

tử số: $2^{12}\cdot3^5-4^6\cdot9^2=2^{12}\cdot3^5-\left(2^2\right)^6\cdot\left(3^2\right)^2$

=$2^{12}\cdot3^5-2^{12}\cdot3^4=2^{12}\cdot3^4\cdot\left(3-1\right)=2^{13}\cdot3^4$

mẫu số: $\left(2^2\cdot3\right)^6+8^4\cdot3^5=\left(2^2\right)^6\cdot3^6+\left(2^3\right)^4\cdot3^5$

=$2^{12}\cdot3^6+2^{12}\cdot3^5=2^{12}\cdot3^5\cdot\left(3+1\right)=2^{14}\cdot3^5$

rút gọn phân số thứ 1:

$\frac{2^{13}\cdot3^4}{2^{14}\cdot3^5}=\frac{1}{2\cdot3}=\frac16$

xét phân số thứ 2:

tử số: $5^{10}\cdot7^3-25^5\cdot49^2=5^{10}\cdot7^3-\left(5^2\right)^5\cdot\left(7^2\right)^2$

=$5^{10}\cdot7^3-5^{10}\cdot7^4=5^{10}\cdot7^3\cdot\left(1-7\right)=5^{10}\cdot7^3\cdot\left(-6\right)$

mẫu số: $\left(125\cdot7\right)^3+5^9\cdot14^3=\left(5^3\cdot7\right)^3+5^9\cdot\left(2\cdot7\right)^3$

=$\left(5^3\right)^3\cdot7^3+2^3\cdot7^3=5^9\cdot7^3+5^9\cdot2^3\cdot7^3$

=$5^9\cdot7^3\cdot\left(1+2^3\right)=5^9\cdot7^3\cdot9$

rút gọn phân số thứ 2:

$\frac{5^{10}\cdot7^3\cdot\left(-6\right)}{5^9\cdot7^3\cdot9}=\frac{5\cdot\left(-6\right)}{9}=-\frac{10}{3}$

cộng hai phân số lại:

A=$\frac16-\frac{-10}{3}=\frac16+\frac{10}{3}=\frac{21}{6}=\frac72$

b) gọi biểu thức cần cm là:

B=$3^{n+2}-2^{n+2}+3^{n}-2^{n}$

=$\left(3^{n+2}+3^{n}\right)-\left(2^{n+2}+2^{n}\right)$

=$\left(3^{n}\cdot9+3^{n}\right)-\left(2^{n}\cdot4+2^{n}\right)$

$=3^{n}\left(9+1\right)-2^{n}\left(4+1\right)$

=$3^{n}\cdot10-2^{n}\cdot5$

mà $3^{n}\cdot10$ ⋮10

$2^{n}\cdot5$ ( vì $n\ge1)$

=> $2^{n}\cdot5=2^{n-1}\cdot2\cdot5=2^{n-1}\cdot10$ ⋮10

=> B⋮10 với mọi số nguyên dương n

Câu trả lời:

xét phân số thứ nhất:

tử số: $2^{12}\cdot3^5-4^6\cdot9^2=2^{12}\cdot3^5-\left(2^2\right)^6\cdot\left(3^2\right)^2$

=$2^{12}\cdot3^5-2^{12}\cdot3^4=2^{12}\cdot3^4\cdot\left(3-1\right)=2^{13}\cdot3^4$

mẫu số: $\left(2^2\cdot3\right)^6+8^4\cdot3^5=\left(2^2\right)^6\cdot3^6+\left(2^3\right)^4\cdot3^5$

=$2^{12}\cdot3^6+2^{12}\cdot3^5=2^{12}\cdot3^5\cdot\left(3+1\right)=2^{14}\cdot3^5$

rút gọn phân số thứ 1:

$\frac{2^{13}\cdot3^4}{2^{14}\cdot3^5}=\frac{1}{2\cdot3}=\frac16$

xét phân số thứ 2:

tử số: $5^{10}\cdot7^3-25^5\cdot49^2=5^{10}\cdot7^3-\left(5^2\right)^5\cdot\left(7^2\right)^2$

=$5^{10}\cdot7^3-5^{10}\cdot7^4=5^{10}\cdot7^3\cdot\left(1-7\right)=5^{10}\cdot7^3\cdot\left(-6\right)$

mẫu số: $\left(125\cdot7\right)^3+5^9\cdot14^3=\left(5^3\cdot7\right)^3+5^9\cdot\left(2\cdot7\right)^3$

=$\left(5^3\right)^3\cdot7^3+2^3\cdot7^3=5^9\cdot7^3+5^9\cdot2^3\cdot7^3$

=$5^9\cdot7^3\cdot\left(1+2^3\right)=5^9\cdot7^3\cdot9$

rút gọn phân số thứ 2:

$\frac{5^{10}\cdot7^3\cdot\left(-6\right)}{5^9\cdot7^3\cdot9}=\frac{5\cdot\left(-6\right)}{9}=-\frac{10}{3}$

cộng hai phân số lại:

A=$\frac16-\frac{-10}{3}=\frac16+\frac{10}{3}=\frac{21}{6}=\frac72$

b) gọi biểu thức cần cm là:

B=$3^{n+2}-2^{n+2}+3^{n}-2^{n}$

=$\left(3^{n+2}+3^{n}\right)-\left(2^{n+2}+2^{n}\right)$

=$\left(3^{n}\cdot9+3^{n}\right)-\left(2^{n}\cdot4+2^{n}\right)$

$=3^{n}\left(9+1\right)-2^{n}\left(4+1\right)$

=$3^{n}\cdot10-2^{n}\cdot5$

mà $3^{n}\cdot10$ ⋮10

$2^{n}\cdot5$ ( vì $n\ge1)$

=> $2^{n}\cdot5=2^{n-1}\cdot2\cdot5=2^{n-1}\cdot10$ ⋮10

=> B⋮10 với mọi số nguyên dương n

Anhhh Duc (Bốp) · Answer

cảm ơn bn nha

Câu trả lời:

cảm ơn bn nha

Nguyễn Lê Phước Thịnh · Answer

a: $\frac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\cdot3\right)^6+8^4\cdot3^5}$

$=\frac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}$

$=\frac{2^{12}\cdot3^4\cdot\left(3-1\right)}{2^{12}\cdot3^5\cdot\left(3+1\right)}=\frac13\cdot\frac24=\frac13\cdot\frac12=\frac16$

Ta có: $\frac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}$

$=\frac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot7^3\cdot2^3}$

$=\frac{5^{10}\cdot7^3\cdot\left(1-7\right)}{5^9\cdot7^3\cdot\left(1+2^3\right)}=5\cdot\frac{-6}{9}=\frac{-30}{9}=\frac{-10}{3}$

TA có: $A=\frac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\cdot3\right)^6+8^4\cdot3^5}-\frac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}$

$=\frac16+\frac{10}{3}=\frac{21}{6}=\frac72$

b: $3^{n+2}-2^{n+2}+3^{n}-2^{n}$

$=3^{n}\cdot9+3^{n}-2^{n}\cdot4-2^{n}$

$=3^{n}\cdot\left(9+1\right)-2^{n}\left(4+1\right)=3^{n}\cdot10-2^{n}\cdot5$

$=3^{n}\cdot10-2^{n-1}\cdot10=10\left(3^{n}-2^{n-1}\right)$ ⋮10

Câu trả lời:

a: $\frac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\cdot3\right)^6+8^4\cdot3^5}$

$=\frac{2^{12}\cdot3^5-2^{12}\cdot3^4}{2^{12}\cdot3^6+2^{12}\cdot3^5}$

$=\frac{2^{12}\cdot3^4\cdot\left(3-1\right)}{2^{12}\cdot3^5\cdot\left(3+1\right)}=\frac13\cdot\frac24=\frac13\cdot\frac12=\frac16$

Ta có: $\frac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}$

$=\frac{5^{10}\cdot7^3-5^{10}\cdot7^4}{5^9\cdot7^3+5^9\cdot7^3\cdot2^3}$

$=\frac{5^{10}\cdot7^3\cdot\left(1-7\right)}{5^9\cdot7^3\cdot\left(1+2^3\right)}=5\cdot\frac{-6}{9}=\frac{-30}{9}=\frac{-10}{3}$

TA có: $A=\frac{2^{12}\cdot3^5-4^6\cdot9^2}{\left(2^2\cdot3\right)^6+8^4\cdot3^5}-\frac{5^{10}\cdot7^3-25^5\cdot49^2}{\left(125\cdot7\right)^3+5^9\cdot14^3}$

$=\frac16+\frac{10}{3}=\frac{21}{6}=\frac72$

b: $3^{n+2}-2^{n+2}+3^{n}-2^{n}$

$=3^{n}\cdot9+3^{n}-2^{n}\cdot4-2^{n}$

$=3^{n}\cdot\left(9+1\right)-2^{n}\left(4+1\right)=3^{n}\cdot10-2^{n}\cdot5$

$=3^{n}\cdot10-2^{n-1}\cdot10=10\left(3^{n}-2^{n-1}\right)$ ⋮10

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