Chứng minh rằng nếu \(\text{ax}^3=by^3=cz^3\) và \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1\) thì
\(\sqrt[3]{\text{ax}^2+by^2+cz^2}=\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}\)
Chứng minh : Nếu \(ax^3=by^3=cz^3\) và \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1\)
thì \(\sqrt[3]{ax^2+by^2+cz^2}=\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}\).
Cho \(ax^3=by^3=cz^3\)và\(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1\)
Chứng minh rằng \(\sqrt[3]{ax^3+by^3+cz^3}=\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}\)
cho \(ax^3=by^3=cz^3\)và \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1\)
CMR: \(\sqrt[3]{ax^2+by^2+cz^2}=\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}\)
cho \(ax^2=by^2=cz^2\)và \(\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1\)cmr:
\(\sqrt[3]{ax^2+by^2+cz^2}=\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}\)
cho \(ax^3=by^3=cz^3;\dfrac{1}{x}+\dfrac{1}{y}+\dfrac{1}{z}=1\). chứng minh \(\sqrt[3]{ax^2+by^2+cz^2}=\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}\)
Cuộc thi toán :^^:
Ko ns nhiều:
1 \(Cho:ax^3=by^3=cz^3.Và:\frac{1}{x}+\frac{1}{y}+\frac{1}{z}=1.CM:\sqrt[3]{a}+\sqrt[3]{b}+\sqrt[3]{c}=\sqrt[3]{ax^2+by^2+cz^2}\)
2. \(CMR:nếu:\frac{x^2-yz}{x\left(1-yz\right)}=\frac{y^2-xz}{y\left(1-xz\right)}.x\ne y;zyx\ne0;yz\ne1;zx\ne1.\Rightarrow xy+yz+zx=xyz\left(x+y+z\right)\)
Cho \(\frac{a}{x}=\frac{b}{y}=\frac{c}{z}\)CMR :
\(\sqrt[3]{ax}+\sqrt[3]{by}+\sqrt[3]{cz}=\sqrt[3]{\left(a+b+c\right)\left(x+y+z\right)}\)
Nếu \(a,b,c\ge0;ax^4=by^4=cz^4;\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}=1\) thì
\(\sqrt{ax^2+by^2+cz^2}=\sqrt{a}+\sqrt{b}+\sqrt{c}\)