Cho P=\(P=\sqrt{x^2+\sqrt[3]{x^4y^2}}+\sqrt{y^2+\sqrt[3]{x^2y^4}}\). Chứng minh rằng: \(\sqrt[3]{P^2}=\sqrt[3]{x^2}+\sqrt[3]{y^2}\)
cho \(a=\sqrt{x^2+\sqrt[3]{x^4y^2}}+\sqrt{y^2+\sqrt[3]{x^2y^4}}\) chứng minh rằng \(\sqrt[3]{a^2}=\sqrt[3]{x^2}+\sqrt[3]{y^2}\)
Chứng minh nếu \(\sqrt{x^2+\sqrt[3]{x^4y^2}}+\sqrt{y^2+\sqrt[3]{x^2y^4}}=a\) thì \(\sqrt[3]{x^2}+\sqrt[3]{y^2}=\sqrt[3]{a^2}\)
Cho \(\sqrt{x^2+\sqrt[3]{x^4}y^2}+\sqrt{y^2+\sqrt[3]{x^2y^4}=a}\)
Chứng minh rằng: \(\sqrt[3]{x^2}+\sqrt[3]{y^2}=\sqrt[3]{a^2}\)
Chứng minh răng nếu: \(\sqrt{x^2+\sqrt[3]{x^4y^2}}+\sqrt{y^2+\sqrt[3]{x^2y^4}}=3\)thì \(\sqrt[3]{x^2}+\sqrt[3]{y^2}=\sqrt[3]{9}\)
cho \(\sqrt{x^2+\sqrt[3]{x^4y^2}}+\sqrt{y^2+\sqrt[3]{x^2y^4}}=a\)
Cmr \(\sqrt[3]{x^2}+\sqrt[3]{y^2}=\sqrt[3]{a^2}\)
cho \(\sqrt{x^2+\sqrt[3]{x^4y^2}}+\sqrt{y^2+\sqrt[3]{x^2y^4}}=a\)
CMR: \(\sqrt[3]{x^2}+\sqrt[3]{y^2}=\sqrt[3]{a^2}\)
Đặt * \(\sqrt[3]{x^2}=m\Rightarrow x^2=m^3\)
* \(\sqrt[3]{y^2}=n\Rightarrow y^2=n^3\)
Áp dụng vào biểu thức trên, ta có:
\(\sqrt{x^2+\sqrt[3]{x^4y^2}}+\sqrt{y^2+\sqrt[3]{x^2y^4}}=a\)
\(\Rightarrow\sqrt{m^3+m^2n}+\sqrt{n^3+n^2m}=a\left(1\right)\)
Bình phương 2 vế, ta được:
\(\left(1\right)\Leftrightarrow m^3+n^3+mn\left(m+n\right)+2\sqrt{m^2n^2\left(m+n\right)}=a^2\)
\(\Leftrightarrow m^3+n^3+3mn\left(m+n\right)=a^2\)
\(\Leftrightarrow\left(m+n\right)^3=a^2\)
\(\Leftrightarrow m+n=\sqrt[3]{a^2}\)
\(\Leftrightarrow\sqrt[3]{x^2}+\sqrt[3]{y^2}=\sqrt[3]{a^2}\left(đpcm\right)\)
(Chúc bạn học giỏi nha!)
chúng minh rằng nếu : \(\sqrt{x^2+\sqrt[3]{x^2y^4}}+\sqrt{y^2+\sqrt[3]{x^2y^4}}=a\) thì \(\sqrt[3]{x^2}+\sqrt[3]{y^2}=\sqrt[3]{a^2}\)
cho \(\sqrt{x^2+\sqrt[3]{x^4y^2}}+\sqrt{y^2+\sqrt[3]{x^2y^4}}=a\)
CMR: \(\sqrt[3]{x^2}+\sqrt[3]{y^2}=\sqrt[3]{a^2}\)
\(\sqrt{x^2+\sqrt[3]{x^4y^2}}+\sqrt{y^2+\sqrt[3]{x^2y^4}}=a\)
CMR:\(\sqrt[3]{x^2}+\sqrt[3]{y^2}=\sqrt[3]{a^2}\)