Ta có:\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\Rightarrow\frac{a^4}{c^4}=\frac{b^4}{d^4}=\frac{a^4+b^4}{c^4+d^4}\left(1\right)\)
Lại có: \(\frac{a}{c}=\frac{b}{d}=\frac{a-b}{c-d}\Rightarrow\frac{a^4}{c^4}=\frac{b^4}{d^4}=\left(\frac{a-b}{c-d}\right)^4\left(2\right)\)
Từ (1) và (2) => đpcm
Cho \(\frac{a}{b}=\frac{c}{d}\)
CMR : \(\frac{\left(a-b\right)^{\text{4}}}{\left(c-d\right)^4}=\frac{a^4+b^4}{c^4+d^4}\)a,b,c,d khác 0
Cho \(\frac{a}{b}\)= \(\frac{c}{d}\)CMR
a) \(\frac{a^2+b^2}{a^2+d^2}\)= \(\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\)
b) \(\left(\frac{a-b}{c-d}\right)^4\)= \(\frac{a^4+b^4}{c^4+d^4}\)
Cho \(\frac{a}{b}\)= \(\frac{c}{d}\) CMR:
a) \(\frac{a^2+b^2}{a^2+d^2}\)= \(\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\)
b) \(\left(\frac{a-b}{c-d}\right)^4\)= \(\frac{a^4+b^4}{c^4+d^4}\)
CMR nếu \(\frac{a}{b}=\frac{c}{d}\)thì \(\left(\frac{a-b}{c-d}\right)^4=\frac{a^4+b^4}{c^4+d^4}\)
1/ Biết \(\frac{a}{b}=\frac{c}{d}\), chứng minh
a) \(\frac{a^2+b^2}{c^2+d^2}=\frac{\left(a+b\right)^2}{\left(c+d\right)^2}\)
b) \(\left(\frac{a-d}{c-b}\right)^4=\frac{a^4+b^4}{c^4+d^4}\)
2/ Cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\)
Chứng minh \(\left(\frac{a+b+c}{b+c+d}\right)^3=\frac{a}{b}\)
3/ Cho \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\)
Chứng minh a=b=c
Cho a,b,c,d,e thỏa mãn:
\(\frac{a}{b}\)= \(\frac{c}{d}\)= \(\frac{b}{c}\)= \(\frac{d}{e}\)CMR:
a) \(\frac{a}{e}\)= \(\left(\frac{a+b+c+d}{b+c+d+e}\right)\)
b) \(\frac{a}{e}\)= \(\frac{a^4+b^4+c^4}{a^4+c^4+d^4+e^4}\)
CHO A/B=C/D CHỨNG MINH RẰNG
\(\frac{\left(a-c\right)^4}{\left(b-d\right)^4}=\frac{5a^4+7c^4}{5b^4+7d^4}\)
\(\frac{a+2c}{b+2d}=\frac{a-3c}{b-3d}\)
\(\frac{a^{2016}+c^{2016}}{b^{2016}+d^{2016}}=\frac{\left(a-c\right)^{2016}}{\left(b-d\right)^{2016}}\)
AI LÀM ĐƯỢC CÂU NÀO CŨNG ĐC,GIÚP MÌNH VS GẤP LẮM,THANKS
Cho 4 số a, b, c, d thỏa mãn: \(b=\frac{a+c}{2};\frac{1}{c}=\frac{1}{2}.\left(\frac{1}{b}+\frac{1}{d}\right)\)
CMR 4 số a, b, c, d lập được thanh 1 tỉ lệ thức
Cho các số dương a, b, c, d thỏa mãn điều kiện a^2+b^2=1 và \(\frac{a^4}{b}+\frac{c^4}{d}=\frac{1}{b+d}\)
CMR \(\frac{a^{2006}}{b^{1003}}+\frac{c^{2006}}{d^{1003}}=\frac{2}{\left(b+d\right)^{1003}}\)
