Đặt : \(\frac{a}{b}=\frac{c}{d}=k\)
\(\Rightarrow a=bk;c=dk\)
\(\Rightarrow\frac{7b^2k^2+3bkb}{11b^2k^2-8b^2}=\frac{7d^2k^2+3dkd}{11d^2k^2-8d^2}\)
\(\Rightarrow\frac{b^2\left(7k^2+3k\right)}{b^2\left(11k^2-8\right)}=\frac{d^2\left(7k^2+3k\right)}{d^2\left(11k^2-8\right)}\)
\(\Rightarrow\frac{7k^2+3k}{11k^2-8}=\frac{7k^2+3k}{11k^2-8}\left(đpcm\right)\)
cho \(\frac{a}{b}=\frac{c}{d}\)
CMR
a) \(\frac{a+c}{b+d}=\frac{a-c}{b-d}\)
b)\(\frac{a-c}{a+c}=\frac{b-d}{b+d}\)
c)\(\frac{2\cdot a-3.c}{2.a+3\cdot c}=\frac{2\cdot b-3\cdot d}{2.b+3\cdot d}\)
Cho \(\frac{a}{b}\)= \(\frac{c}{d}\), chứng minh \(\frac{5\cdot a+3\cdot b}{5\cdot a-3\cdot b}\)= \(\frac{5\cdot c+3\cdot d}{5\cdot c-3\cdot d}\)
Tìm a, b, c biết: \(\frac{3\cdot a-2\cdot b}{5}=\frac{2\cdot c-5\cdot a}{3}=\frac{5\cdot b-3\cdot c}{2}\)và a+b+c= -50
Tìm 3 số a,b,c biết: \(\frac{3\cdot a-2\cdot b}{5}=\frac{2\cdot c-5\cdot a}{3}=\frac{5\cdot b-3\cdot c}{2}\) và a+b+c=-50
cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}=\frac{d}{a}\)và a+b+c+d khác 0. Tính Q=\(\frac{2\cdot a-b}{c+d}+\frac{2\cdot b-c}{d+a}+\frac{2\cdot c-d}{a+b}+\frac{2\cdot d-a}{b+c}\)
Tính giá trị các biểu thức:
a)\(A=\frac{12}{3\cdot7}+\frac{12}{7\cdot11}+...+\frac{12}{195\cdot199}\)
b)\(B=\frac{3}{4}\cdot\frac{8}{9}\cdot\frac{15}{16}\cdot...\cdot\frac{2499}{2500}\)
c)\(C=\frac{1}{2}-\frac{1}{2^2}+\frac{1}{2^3}-\frac{1}{2^4}+...+\frac{1}{2^{99}}-\frac{1}{2^{100}}\)
tìm x biết
a, \(\frac{1}{2}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot\frac{4}{10}\cdot...\cdot\frac{30}{62}\cdot\frac{31}{64}=4^x\)
b, \(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}\cdot\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=8^x\)
c,\(\left|4x+3\right|-\left|x-1\right|=7\)
mong các bạn giúp !!!
Tính giá trị của biểu thức:
a,(32)2-(-23)2-(-52)3
b,\(\left|\frac{-1}{2}\right|^2\cdot\left(-32\right)-\left(-8\right)+\left|\frac{1}{2}\right|^3\)
c,\(2^3+3\cdot\left(\frac{-5}{86}\right)^0\cdot\left(\frac{1}{2}\right)^2\cdot4+\left[\left(-2\right)^2:\frac{1}{2}\right]:8\)
d,\(\left|\frac{5}{7}\cdot\left(-14\right)\right|-\left(\frac{2}{3}\right)^2\cdot\left(-18\right)+6^2\cdot\frac{-1}{18}\)
TÌM x biết:
a) \(\frac{1}{4}\cdot\frac{2}{6}\cdot\frac{3}{8}\cdot\frac{4}{10}\cdot\frac{5}{12}\cdot...\cdot\frac{30}{62}\cdot\frac{31}{62}=4^x\)
b) \(\frac{4^5+4^5+4^5+4^5}{3^5+3^5+3^5}\cdot\frac{6^5+6^5+6^5+6^5+6^5+6^5}{2^5+2^5}=8^x\)
c)\(\left|4x+3\right|-\left|x-1\right|=7\)
