Cho \(\frac{a+5}{a-5}=\frac{b+6}{b-6}.\) Chứng minh rằng \(\frac{a}{b}=\frac{5}{6}\)
Giúp mk giải nha!!!
Cho \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)\(\) (a khác 5, b khác 6). Chứng minh rằng \(\frac{a}{b}=\frac{5}{6}\)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Rightarrow\left(a+5\right)\left(b-6\right)=\left(a-5\right)\left(b+6\right)\)
\(\Rightarrow ab-6a+5b-30=ab+6a-5b-30\)
\(\Rightarrow5b=6a\Leftrightarrow\frac{a}{b}=\frac{5}{6}\)
(Đpcm)
Từ \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Rightarrow\frac{b-6}{a-5}=\frac{b+6}{a+5}\)
Áp dụng t/c dãy tỉ số bằng nhau :
\(\frac{b-6}{a-5}=\frac{b+6}{a+5}=\frac{\left(b+6\right)-\left(b-6\right)}{\left(a+5\right)-\left(a-5\right)}=\frac{12}{10}=\frac{6}{5}\)
\(\Rightarrow5\left(b-6\right)=6\left(a-5\right)\Leftrightarrow5b=6a\Leftrightarrow\frac{a}{b}=\frac{5}{6}\)
cho \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\) . CHỨNG MINH RẰNG \(\frac{a}{b}=\frac{5}{6}\)
ta có : \(\frac{a+5}{a-5}\)=\(\frac{b+6}{b-6}\)
<=> (a+5)(b-6)=(a-5)(b+6)
<=> ab-6a+5b-30=ab+6a-5b-30
<=>5b+5b=6a+6a
<=> 10b=12a
<=> \(\frac{a}{b}\)=\(\frac{10}{12}\)=\(\frac{5}{6}\)=> đfcm
bạn nhân chéo rồi rút gọn nha
sau đó áp dụng tính chất cuartir lệ thức
59. Cho \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\left(a\ne5;b\ne6\right)\). Chứng minh rằng \(\frac{a}{b}=\frac{5}{6}\)
\(\left(a+5\right)\left(b-6\right)=\left(a-5\right)\left(b+6\right)\)
\(\Leftrightarrow ab-6a+5b-30=ab+6a-5b-30\)
\(\Leftrightarrow ab-ab+5b+5b-30+30=6a+6a\)
\(\Leftrightarrow10b=12a\)
\(\Rightarrow\frac{a}{b}=\frac{10}{12}=\frac{5}{6}\left(đpcm\right)\)
a+5/a-5=b+6/b-6=a+5/b+6=b+6/b-69 (giao hoán trung tỉ)=>(a+5)-5/(b+6)-6=(a+5)-a/(b+6)-6=a/b=5/6
BẠN ƠI CÁI MÀ '/' LÀ PHẦN NHA
cho \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)(\(a\ne5;b\ne6\).chứng minh rằng \(\frac{a}{b}=\frac{5}{6}\)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\Rightarrow\left(a+5\right)\left(b-6\right)=\left(a-5\right)\left(b+6\right)\)
\(\Rightarrow ab-6a+5b-30=ab+6a-5b-30\)
\(\Rightarrow5b=6a\)
\(\Rightarrow\frac{a}{b}=\frac{5}{6}\)
Đpcm
Cho \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\left(a\ne5;b\ne6\right).\)Chứng minh rằng \(\frac{a}{b}=\frac{5}{6}\)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)
<=> \(\frac{a-5+10}{a-5}=\frac{b-6+12}{b-6}\)
<=> \(1+\frac{10}{a-5}=1+\frac{12}{b-6}\)
<=> \(\frac{10}{a-5}=\frac{12}{b-6}\)
<=> 10( b - 6 ) = 12( a - 5 )
<=> 5( b - 6 ) = 6( a - 5 )
<=> 5b - 30 = 6a - 30
<=> 5b = 6a
<=> \(\frac{6}{5}=\frac{b}{a}\)hay \(\frac{a}{b}=\frac{5}{6}\)( đpcm )
Cho \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)(\(a\ne5;b\ne6\))
Chứng minh rằng \(\frac{a}{b}=\frac{5}{6}\)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)
\(\Leftrightarrow\left(a+5\right)\left(b-6\right)=\left(b+6\right)\left(a-5\right)\)
\(\Leftrightarrow ab-6a+5b-30=ab-5b+6a-30\)
\(\Leftrightarrow-6a+5b=6a-5b\)
\(\Leftrightarrow5b+5b=6a+6a\)
\(\Leftrightarrow10b=12a\)
\(\Leftrightarrow\frac{a}{b}=\frac{10}{12}=\frac{5}{6}\)
Cho \(\frac{a+5}{a-5}=\frac{b+6}{b-6}(a\ne5;b\ne6)\)
Chứng minh rằng \(\frac{a}{b}=\frac{5}{6}\)
Ta có: \(\frac{x+5}{x-5}=\frac{b+6}{b-6}\)
\(\Leftrightarrow\left(a+5\right)\left(b-6\right)=\left(a-5\right)\left(b+6\right)\)
\(\Leftrightarrow ab-6a+5b-30=ab+6a-5b-30\)
\(\Leftrightarrow16a=10b\)
\(\Leftrightarrow\frac{a}{b}=\frac{10}{12}=\frac{5}{6}\left(đpcm\right)\)
Cho \(\frac{a+5}{a-5}=\frac{b+6}{b-6}\left(a\ne5;b\ne6\right)\) Chứng minh rằng \(\frac{a}{b}=\frac{5}{6}\)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)
\(\Leftrightarrow\frac{a-5+10}{a-5}=\frac{b-6+12}{b-6}\)
\(\Leftrightarrow1+\frac{10}{a-5}=1+\frac{12}{b-6}\)
\(\Leftrightarrow\frac{10}{a-5}=\frac{12}{b-6}\)
\(\Rightarrow10.\left(b-6\right)=12.\left(a-5\right)\)
\(10b-60=12a-60\)
\(10b=12a\)
\(\frac{a}{b}=\frac{10}{12}=\frac{5}{6}\)
\(\frac{a+5}{a-5}=\frac{b+6}{b-6}\)
\(=>\frac{a+5}{b+6}=\frac{a-5}{b-6}=\frac{a+5-\left(a-5\right)}{b+6-\left(b-6\right)}=\frac{a+5-a+5}{b+6-b+6}=\frac{10}{12}=\frac{5}{6}\)
\(\frac{a+5}{b+6}=\frac{a-5}{b-6}=\frac{a+5+\left(a-5\right)}{b+6+\left(b-5\right)}=\frac{a+5+a-5}{b+6+b-6}=\frac{2a}{2b}=\frac{a}{b}\)
=>\(\frac{a}{b}=\frac{a+5}{b+5}=\frac{5}{6}\)
=>\(\frac{a}{b}=\frac{5}{6}\)
Cho b2 = ac; c2 = bd. Chứng minh rằng:
a,\(\frac{a^3+b^3-c^3}{b^3+c^3-d^3}=\left(\frac{a+b-c}{b+c-d}\right)^3\)
b,\(\frac{3a^2+5b^4-7c^6}{3b^2+5c^4-7d^6}=\frac{2a^3+4b^5-6c^7}{2b^3+4c^5-6d^7}\)
Giúp mk nha, thứ 3 mình nộp ùi
a/ Ta có: \(b^2=ac\Rightarrow\frac{a}{b}=\frac{b}{c};c^2=bd\Rightarrow\frac{b}{c}=\frac{c}{d}\)\(\Rightarrow\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\)
Đặt \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=k\Rightarrow\left(\frac{a}{b}\right)^3=\left(\frac{b}{c}\right)^3=\left(\frac{c}{d}\right)^3=k^3\Rightarrow\frac{a^3}{b^3}=\frac{b^3}{c^3}=\frac{c^3}{d^3}=k^3\)
Áp dụng tính chất của tỉ lệ thức ta có:\(\frac{a^3}{b^3}=\frac{b^3}{c^3}=\frac{c^3}{d^3}=\frac{a^3+b^3+c^3}{b^3+c^3+d^3}=k^3\)
Mặt khác: \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=k\Rightarrow\frac{a+b+c}{b+c+d}=k\Rightarrow\left(\frac{a+b+c}{b+c+d}\right)^3=k^3\)
\(\Rightarrow\frac{a^3+b^3+c^3}{b^3+c^3+d^3}=\left(\frac{a+b+c}{b+c+d}\right)^3\left(=k^3\right)\)
giup minh nha: Tinh nhanh lop 4
42 x 43 - 12 x 9 - 42 x 3