Câu hỏi của Nguyễn Phương Quỳnh Chi

Question

Cho $b^2=ac$ ; $c^2=bd$. Chứng minh rằng:a) $\frac{a^3+b^3-c^3}{b^3+c^3-d^3}=\left(\frac{a+b-c}{b+c-d}\right)^3$b) $\frac{a}{d}=\frac{a^3+8b^3+125c^3}{b^2+8c^3+125d^3}$

nameless · Accepted Answer

a) $b^2=ac\Rightarrow b.b=ac\Rightarrow\frac{b}{a}=\frac{c}{b}\Rightarrow\frac{a}{b}=\frac{b}{c}$    $c^2=bd\Rightarrow c.c=bd\Rightarrow\frac{c}{b}=\frac{d}{c}\Rightarrow\frac{b}{c}=\frac{c}{d}$Ngoặc ''}'' 2 điều trên$\Rightarrow\frac{a}{b}=\frac{b}{c}=\frac{c}{d}$$\Rightarrow\left(\frac{a}{b}\right)^3=\left(\frac{b}{c}\right)^3=\left(\frac{c}{d}\right)^3=\left(\frac{a+b-c}{b+c-d}\right)^3$$\Rightarrow\frac{a^3}{b^3}=\frac{b^3}{c^3}=\frac{c^3}{d^3}=\left(\frac{a+b-c}{b+c-d}\right)^3$Vậy ...b) $b^2=ac\Rightarrow b.b=ac\Rightarrow\frac{b}{a}=\frac{c}{b}\Rightarrow\frac{a}{b}=\frac{b}{c}$    $c^2=bd\Rightarrow c.c=bd\Rightarrow\frac{c}{b}=\frac{d}{c}\Rightarrow\frac{b}{c}=\frac{c}{d}$Ngoặc ''}'' 2 điều trên$\Rightarrow\frac{a}{b}=\frac{b}{c}=\frac{c}{d}$$\Rightarrow\left(\frac{a}{b}\right)^3=\left(\frac{b}{c}\right)^3=\left(\frac{c}{d}\right)^3=\frac{a.b.c}{b.c.d}$$\Rightarrow\frac{a^3}{b^3}=\frac{b^3}{c^3}=\frac{c^3}{d^3}=\frac{a}{d}$(Do loại bỏ b.c trên tử + dưới mẫu nên còn a/d)$\Rightarrow\frac{a^3}{b^3}=\frac{8b^3}{3c^3}=\frac{125c^3}{125d^3}=\frac{a}{d}$(Dùng tính chất phân số)Vậy ...P/s: Có gì khó hiểu thì hỏi nhé ^^Câu trả lời: a) $b^2=ac\Rightarrow b.b=ac\Rightarrow\frac{b}{a}=\frac{c}{b}\Rightarrow\frac{a}{b}=\frac{b}{c}$    $c^2=bd\Rightarrow c.c=bd\Rightarrow\frac{c}{b}=\frac{d}{c}\Rightarrow\frac{b}{c}=\frac{c}{d}$Ngoặc ''}'' 2 điều trên$\Rightarrow\frac{a}{b}=\frac{b}{c}=\frac{c}{d}$$\Rightarrow\left(\frac{a}{b}\right)^3=\left(\frac{b}{c}\right)^3=\left(\frac{c}{d}\right)^3=\left(\frac{a+b-c}{b+c-d}\right)^3$$\Rightarrow\frac{a^3}{b^3}=\frac{b^3}{c^3}=\frac{c^3}{d^3}=\left(\frac{a+b-c}{b+c-d}\right)^3$Vậy ...b) $b^2=ac\Rightarrow b.b=ac\Rightarrow\frac{b}{a}=\frac{c}{b}\Rightarrow\frac{a}{b}=\frac{b}{c}$    $c^2=bd\Rightarrow c.c=bd\Rightarrow\frac{c}{b}=\frac{d}{c}\Rightarrow\frac{b}{c}=\frac{c}{d}$Ngoặc ''}'' 2 điều trên$\Rightarrow\frac{a}{b}=\frac{b}{c}=\frac{c}{d}$$\Rightarrow\left(\frac{a}{b}\right)^3=\left(\frac{b}{c}\right)^3=\left(\frac{c}{d}\right)^3=\frac{a.b.c}{b.c.d}$$\Rightarrow\frac{a^3}{b^3}=\frac{b^3}{c^3}=\frac{c^3}{d^3}=\frac{a}{d}$(Do loại bỏ b.c trên tử + dưới mẫu nên còn a/d)$\Rightarrow\frac{a^3}{b^3}=\frac{8b^3}{3c^3}=\frac{125c^3}{125d^3}=\frac{a}{d}$(Dùng tính chất phân số)Vậy ...P/s: Có gì khó hiểu thì hỏi nhé ^^

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