Các câu hỏi tương tự
Chứng minh rằng nếu a/b=c/d\(a,\frac{a^2+2c^2}{b^2+2d^2}=\left(\frac{a+3c}{b+3d}\right)^2\) \(\frac{a^{2016}+3b^{2016}}{c^{2016}+3d^{2016}}=\left(\frac{a^2+2b^2}{c^2+2d^2}\right)^2\)
Cho \(\frac{a}{b}=\frac{c}{d}\)Chứng minh rằng:
a) \(\frac{\left(2a+3b\right)^2}{\left(3a-4b\right)^2}=\frac{\left(2c+3d\right)^2}{\left(3c-4d\right)^2}\)
b) \(\frac{2a^2-3ab+4b^2}{2b^2+5ab}=\frac{2c^2-3cd+4d^2}{2d^2+5cd}\)
Cho \(\frac{a}{b}=\frac{c}{d}\)
a) Chứng minh \(\frac{3a+2c}{3d+2d}=\frac{3c-5a}{3d-5b}\)
b) Chứng minh \(\frac{a^2}{b^2}=\frac{2c^2-ac}{2d^2-bd}\)
Cho \(\frac{a}{b}=\frac{c}{d}\), chứng minh rằng:
\(\frac{\left(a-b\right)^3}{\left(c-d\right)^3}=\frac{3a^2+2b^2}{3c^2+2d^2}\)
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 các số thực a,b,c,d khác 0 thỏa mãn \(\frac{a}{b}=\frac{b}{c}=\frac{c}{d}.\)Chứng minh rằng
\(\frac{a^3+2b^3+3c^3}{b^3+2c^3+3d^3}=\left(\frac{a+2b+3c}{b+2c+3d}\right)^3=\frac{a}{d}\)
Cho \(\frac{a}{b}=\frac{c}{d}\)CMR:
a,\(\frac{2a^2-3b^2}{2c^2-3d^2}=\frac{ab}{cd}\)
b,\(\frac{ab}{cd}=\frac{\left(a-2b\right)^2}{\left(c-2d\right)^2}\)
Đặtfrac{a}{b}frac{c}{d}kabk ; cdkVT frac{3a^2-4ab+5b^2}{2b^2+3ab}frac{3b^2k^2-4b^2k+5b^2}{2b^2+3b^2k}frac{b^2left(3k^2-4k+5right)}{b^2left(2+3kright)}frac{3k^2-4k+5}{2+3k}VP frac{3c^2-4cd+5d^2}{2c^2+3cd}frac{3d^2k^2-4d^2k+5d^2}{2d^2+3d^2k}frac{d^2left(3k^2-4k+5right)}{d^2left(2+3kright)}frac{3k^2-4k+5}{2+3k}nhận thấy VTVP suy ra đpcm
Đọc tiếp
Đặt\(\frac{a}{b}=\frac{c}{d}=k\)=>a=bk ; c=dk
VT= \(\frac{3a^2-4ab+5b^2}{2b^2+3ab}=\frac{3b^2k^2-4b^2k+5b^2}{2b^2+3b^2k}=\frac{b^2\left(3k^2-4k+5\right)}{b^2\left(2+3k\right)}=\frac{3k^2-4k+5}{2+3k}\)
VP = \(\frac{3c^2-4cd+5d^2}{2c^2+3cd}=\frac{3d^2k^2-4d^2k+5d^2}{2d^2+3d^2k}=\frac{d^2\left(3k^2-4k+5\right)}{d^2\left(2+3k\right)}=\frac{3k^2-4k+5}{2+3k}\)
nhận thấy VT=VP suy ra đpcm
Cho frac{a}{b}frac{c}{d}. Chứng minh:a) frac{left(a-bright)^3}{left(c-dright)^3}frac{3a^2+2b^2}{3c^2+2d^2}b)frac{4a^4+5b^4}{4c^4+5d^4}frac{a^2b^2}{c^2d^2}c)left(frac{a-b}{c-d}right)^{2005}frac{2a^{2005}-b^{2005}}{2c^{2005}-d^{2005}}d)frac{2a^{2005}+5b^{2005}}{2c^{2005}+5d^{2005}}frac{left(a+bright)^{2005}}{left(c+dright)^{2005}}e)frac{left(20a^{2006}+11b^{2006}right)^{2007}}{left(20a^{2007}-11b^{2007}right)^{2006}}frac{left(20c^{2006}+11d^{2006}right)^{2007}}{left(20c^{2007}-11d^{2007}right)^{20...
Đọc tiếp
Cho \(\frac{a}{b}=\frac{c}{d}\). Chứng minh:
a) \(\frac{\left(a-b\right)^3}{\left(c-d\right)^3}=\frac{3a^2+2b^2}{3c^2+2d^2}\)
b)\(\frac{4a^4+5b^4}{4c^4+5d^4}=\frac{a^2b^2}{c^2d^2}\)
c)\(\left(\frac{a-b}{c-d}\right)^{2005}=\frac{2a^{2005}-b^{2005}}{2c^{2005}-d^{2005}}\)
d)\(\frac{2a^{2005}+5b^{2005}}{2c^{2005}+5d^{2005}}=\frac{\left(a+b\right)^{2005}}{\left(c+d\right)^{2005}}\)
e)\(\frac{\left(20a^{2006}+11b^{2006}\right)^{2007}}{\left(20a^{2007}-11b^{2007}\right)^{2006}}=\frac{\left(20c^{2006}+11d^{2006}\right)^{2007}}{\left(20c^{2007}-11d^{2007}\right)^{2006}}\)
f)\(\frac{\left(20a^{2007}-11c^{2007}\right)^{2006}}{\left(20a^{2006}+11c^{2006}\right)^{2007}}=\frac{\left(20b^{2007}-11d^{2007}\right)^{2006}}{\left(20b^{2006}+11d^{2006}\right)^{2007}}\)