cho a/b=b/c=c/d chung minh rằng a^3+c^3-b^3/c^3+b^3-d^3=a/d
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Cho a/b = b/c = c/d (b,c,d # 0). Chung minh rang
a^3 + b^3 + c^3/ b^3+ c^3 + d^3 =a/b
6 tháng 11 2021 lúc 20:31
Cho b^2 = ac ; c^2 = bd với b, c, d ≠ 0; b+c ≠ 0; b^3+c^3≠ d^3 3. Chứng minh rằng:
a) \(\dfrac{a^3+b^3-c^3}{b^3+c^3-d^3}=\left(\dfrac{a+b-c}{b+c-d}\right)^3\)
b) \(\dfrac{a^3+b^3+c^3}{b^3+c^3+d^3}=\dfrac{a}{d}\)
7 tháng 11 2021 lúc 14:13
Cho \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}\) Chứng minh rằng \(\dfrac{a^3+b^3+c^3}{b^3+c^3+d^3}=\dfrac{a}{d}\)
Đặt \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}=k\)
\(\Leftrightarrow\left\{{}\begin{matrix}a=bk\\b=ck\\c=dk\end{matrix}\right.\)
Ta có: \(\dfrac{a^3+b^3+c^3}{b^3+c^3+d^3}=\dfrac{b^3k^3+c^3k^3+d^3k^3}{b^3+c^3+d^3}=k^3\)
\(\dfrac{a}{d}=\dfrac{bk}{d}=\dfrac{ck^2}{d}=\dfrac{dk^3}{d}=k^3\)
Do đó: \(\dfrac{a^3+b^3+c^3}{b^3+c^3+d^3}=\dfrac{a}{d}\)
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Cho \(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}\) chung minh rang \(\dfrac{a^3+b^3+c^3}{a^3+c^3+d^3}=\dfrac{a}{d}\)
Ta co :\(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}\)=>\(\left(\dfrac{a}{b}\right)^3=\left(\dfrac{b}{c}\right)^3=\left(\dfrac{c}{d}\right)^3\)
=> \(\dfrac{a^3}{b^3}=\dfrac{b^3}{c^3}=\dfrac{c^3}{d^3}=\dfrac{a^3+b^3+c^3}{b^3+c^3+d^3}\) (1)
Mặt khác:\(\dfrac{a^3}{b^3}=\dfrac{a}{b}.\dfrac{b}{c}.\dfrac{c}{d}=\dfrac{a}{d}\) (2)
Tu (1) va (2)
=> \(\dfrac{a^3+b^3+c^3}{b^3+c^3+d^3}=\dfrac{a}{d}\) (dpcm)
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cho a/c=c/b=b/d. chứng minh rằng a^3+c^3-b^3/c^3+b^3-d^3=a/d
Cho a/b=b/c .Chứng minh rằng: (a-b/c-d)^3=a^3-b^3/c^3-d^3
30 tháng 10 2021 lúc 21:49
Cho a, b, c, d là 4 số khác 0 thỏa mãn \(b^2\) = ac; \(c^2\) = bd và \(b^3+c^3+d^3\ne0\)
Chứng minh rằng: \(\dfrac{a}{d}=\dfrac{a^3+b^3+c^3}{b^3+c^3+d^3}=\left(\dfrac{a+b+c}{b+c+d}\right)^3\)
Cho a/c=c/d=b/d .Chứng minh rằng a^3+c^3-b^3/c^3+b^3-d^3
cho a/b = b/c = c/d . chứng minh rằng ( a+b+c/b+c+d ) 3 3 = a/d
\(\dfrac{a}{b}.\dfrac{b}{c}.\dfrac{c}{d}=\dfrac{a}{d}\) ; \(\dfrac{a}{b}.\dfrac{b}{c}.\dfrac{c}{d}=\dfrac{a}{b}.\dfrac{a}{b}.\dfrac{a}{b}=\dfrac{a^3}{b^3}\)
\(\dfrac{a}{b}=\dfrac{b}{c}=\dfrac{c}{d}=\dfrac{a+b+c}{b+c+d}\)
\(\Rightarrow\dfrac{a^3}{b^3}=\dfrac{\left(a+b+c\right)^3}{\left(b+c+d\right)^3}=\dfrac{a}{d}\).
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