CMR Nếu \(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a^{2014}+b^{2014}}{c^{2014}+d^{2014}}=\frac{\left(a-b\right)^{2014}}{\left(c-d\right)^{2014}}\)
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cho tỉ lệ thức a/b= c/d với a.b,c,d khác 0 và c khác -d . CMR :\(\frac{\left(a+b\right)^{2014}}{\left(c+d\right)^{2014}}=\frac{a^{2014}+b^{2014}}{c^{2014}+d^{2014}}\)
Chứng minh rằng : Nếu \(\frac{a}{b}=\frac{c}{d}\) thì \(\left(\frac{a-c}{c-d}\right)^{2014}=\frac{a^{2014}+b^{2014}}{c^{2014}+d^{2014}}\)
Cho tỉ lệ thức: a/b = c/d . chứng minh rằng: \(\frac{a^{2014}+c^{2014}}{b^{2014}+a^{2014}}=\frac{\left(a+c\right)^{2014}}{\left(b+d\right)^{2014}}\)
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Chứng minh rằng: Nếu a/b=c/d thì \(\frac{a^{2014}+b^{2014}}{c^{2014}+d^{2014}}=\left(\frac{a-b}{c-d}\right)^{2014}\)
\(\frac{a}{b}=\frac{c}{d}\Rightarrow\frac{a}{c}=\frac{b}{d}\) Theo t/c dãy tỷ số băng nhau ta có
\(\frac{a}{c}=\frac{b}{d}=\frac{a-b}{c-d}\Rightarrow\left(\frac{a-b}{c-d}\right)^{2014}=\frac{a^{2014}}{c^{2014}}=\frac{b^{2014}}{d^{2014}}\) Theo t/c dãy tỷ số bằng nhau
\(\left(\frac{a-b}{c-d}\right)^{2014}=\frac{a^{2014}+b^{2014}}{c^{2014}+d^{2014}}\) (dpcm)
v~ cay wa đề mình là (a+b)^2014/(c+d)^2014= a^2014+b^2014/ c^2014+d^2014
chứng minh rằng: Nếu \(\frac{a}{b}=\frac{c}{d}\) thì \(\frac{a^{2014}+b^{2014}}{c^{2014}+d^{2014}}=\left(\frac{a-b}{c-d}\right)^{2014}\)
a/b=c/d=>a/c=b/d(theo tính chất dãy tỉ số bằng nhau)
a/c=b/d=a-b/c-d=>(a-b/c-d)2014=a2014/c2014=b2014/d2014(theo t/c dãy tỉ số = nhau)
tick cho mình nha mèo
So sánh a) A=\(\frac{10^7+5}{10^7+8}\) và B=\(\frac{10^8+6}{10^8-7}\)
CMR:nếu \(\frac{a}{b}=\frac{c}{d}\) thì\(\left(\frac{a-b}{c-d}\right)^{2014}=\frac{a^{2014}+b^{2014}}{c^{2014}+d^{2014}}\)
GIÚP MÌNH VỚI MỌI NGƯỜI ƠI
CMR : Nếu \(\dfrac{a}{b}=\dfrac{c}{d}th\text{ì}\dfrac{a^{2014}+b^{2014}}{c^{2014}+d^{2014}}=\left(\dfrac{a-b}{c-d}\right)^{2014}\)
CMR: Nếu \(\dfrac{a}{b}=\dfrac{c}{d}\)thì \(\dfrac{a^{2014}+b^{2014}}{c^{2014}+d^{2014}}=\left(\dfrac{a-b}{c-d}\right)^{2014}\)
\(\dfrac{a}{b}=\dfrac{c}{d}=k\\ \Rightarrow a=bk;c=dk\\ \dfrac{a^{2014}+b^{2014}}{c^{2014}+d^{2014}}=\dfrac{\left(bk\right)^{2014}+b^{2014}}{\left(dk\right)^{2014}+d^{2014}}=\dfrac{b^{2014}\left(k^{2014}+1\right)}{d^{2014}\left(k^{2014}+1\right)}=\dfrac{b^{2014}}{d^{2014}}\\ \left(\dfrac{a-b}{c-d}\right)^{2014}=\left(\dfrac{bk-b}{dk-d}\right)^{2014}=\left(\dfrac{b\left(k-1\right)}{d\left(k-1\right)}\right)^{2014}=\left(\dfrac{b}{d}\right)^{2014}=\dfrac{b^{2014}}{d^{2014}}\\ \RightarrowĐPCM\)
CMR: Nếu \(\dfrac{a}{b}=\dfrac{c}{d}\) thì \(\left(\dfrac{a-b}{c-d}\right)^{2014}=\dfrac{a^{2014}+b^{2014}}{c^{2014}+d^{2014}}\)
Đặt \(\dfrac{a}{b}=\dfrac{c}{d}=k\)\(\Rightarrow a=bk;c=dk\)
Xét \(VT=\left(\dfrac{a-b}{c-d}\right)^{2014}=\left(\dfrac{bk-b}{dk-d}\right)^{2014}=\left(\dfrac{b\left(k-1\right)}{d\left(k-1\right)}\right)^{2014}=\left(\dfrac{b}{d}\right)^{2014}\left(1\right)\)
Xét \(VP=\dfrac{a^{2014}+b^{2014}}{c^{2014}+d^{2014}}=\dfrac{b^{2014}k^{2014}+b^{2014}}{d^{2014}k^{2014}+d^{2014}}=\dfrac{b^{2014}\left(k^{2014}+1\right)}{d^{2014}\left(k^{2014}+1\right)}=\dfrac{b^{2014}}{d^{2014}}=\left(\dfrac{b}{d}\right)^{2014}\left(2\right)\)
Từ \(\left(1\right);\left(2\right)\) ta có ĐPCM