Lời giải:
\((x^2-1)(x^2-25)=25x^2\)
\(\Leftrightarrow x^4-26x^2+25=25x^2\)
\(\Leftrightarrow x^4-51x^2+25=0\)
\(\Leftrightarrow a^2-51a+25=0\) (đặt \(a=x^2)\)
\(\Leftrightarrow (a-\frac{51}{2})^2=\frac{2501}{4}\Rightarrow a-\frac{51}{2}=\pm \frac{\sqrt{2501}}{2}\)
\(\Rightarrow a=\frac{51\pm \sqrt{2501}}{2}\)
\(\Rightarrow x=\pm \sqrt{\frac{51\pm \sqrt{2501}}{2}}\)
Lời giải:
\((x^2-1)(x^2-25)=25x^2\)
\(\Leftrightarrow x^4-26x^2+25=25x^2\)
\(\Leftrightarrow x^4-51x^2+25=0\)
\(\Leftrightarrow a^2-51a+25=0\) (đặt \(a=x^2)\)
\(\Leftrightarrow (a-\frac{51}{2})^2=\frac{2501}{4}\Rightarrow a-\frac{51}{2}=\pm \frac{\sqrt{2501}}{2}\)
\(\Rightarrow a=\frac{51\pm \sqrt{2501}}{2}\)
\(\Rightarrow x=\pm \sqrt{\frac{51\pm \sqrt{2501}}{2}}\)
Lời giải:
\((x^2-1)(x^2-25)=25x^2\)
\(\Leftrightarrow x^4-26x^2+25=25x^2\)
\(\Leftrightarrow x^4-51x^2+25=0\)
\(\Leftrightarrow a^2-51a+25=0\) (đặt \(a=x^2)\)
\(\Leftrightarrow (a-\frac{51}{2})^2=\frac{2501}{4}\Rightarrow a-\frac{51}{2}=\pm \frac{\sqrt{2501}}{2}\)
\(\Rightarrow a=\frac{51\pm \sqrt{2501}}{2}\)
\(\Rightarrow x=\pm \sqrt{\frac{51\pm \sqrt{2501}}{2}}\)
Đặt \(x^2-1=a\Rightarrow x^2=a+1\)
\(PT\Leftrightarrow a\left(a-24\right)=25\left(a+1\right)\)
\(\Leftrightarrow a^2-49a-25=0\Leftrightarrow\left(a^2-2.a.\frac{49}{2}+\left(\frac{49}{2}\right)^2-\left(\frac{49}{2}\right)^2-25\right)=0\)
\(\Leftrightarrow\left(a-\frac{49}{2}\right)^2=\frac{2501}{4}\)
Suy ra \(a=\pm\sqrt{\frac{2501}{4}}+\frac{49}{2}\Rightarrow x^2=\pm\frac{\sqrt{2501}}{2}+\frac{51}{2}\)
Suy ra \(x=\pm\sqrt{\frac{51}{2}\pm\frac{\sqrt{2501}}{2}}\)
Số xấu quá -_-"