Question

$x^3-225x=0\\\\x^4-10x^2-24=0$

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Answer 1

$\displaystyle\bf\\1)\\\\x^{3} -225x=0\\\\x\cdot(x^{2} -225)=0\\\\x\cdot(x^{2} -15^{2} )=0\\\\x\cdot(x-15)\cdot(x+15)=0\\\\\\\left[\begin{array}{ccc}x =0\\x-15=0\\x+15=0\end{array}\right\\\\\\\left[\begin{array}{ccc}x_{1} =0\\x_{2} =15\\x_{3} =-15\end{array}\right\\\\\\Otvet \ : \ 0 \ ; \ 15 \ ; \ -15$

$\displaystyle\bf\\2)\\\\x^{4} -10x^{2} -24=0\\\\x^{2} =m \ , \ \ m\geq 0\\\\m^{2} -10m-24=0\\\\D=(-10)^{2} -4\cdot (-24)=100+96=196=14^{2} \\\\\\m_{1} =\frac{10+14}{2} =12\\\\\\m_{2} =\frac{10-14}{2} =-2 < 0 \ -ne \ podxodit\\\\\\x^{2} =12\\\\x_{1,2} =\pm \ \sqrt{12} =\pm \ 2\sqrt{3} \\\\\\Otvet \ : \ -2\sqrt{3} \ ; \ 2\sqrt{3}$