Question

Пожалуйста, решите уравнение.
х^4-х^2/4х^2(х-1)=0

Answer 1

Ответ:

$x = - 1$

Объяснение:

$frac{ {x}^{4} - {x}^{2} }{4 {x}^{2} (x - 1)} = 0 : : : : : : x≠0 : : : : : x≠ 1 \ frac{ {x}^{2}( {x}^{2} - 1) }{4 {x}^{2} (x - 1) } =0 \ frac{ {x}^{2}(x - 1)(x + 1) }{4 {x}^{2}(x -1) } =0 \ frac{x + 1}{4} = 0 \ x + 1 = 0 \ x = - 1$

Answer 2

$displaystyle frac{x^4-x^2}{4x^2(x-1)}=0quadquadquad left[begin{array}{ccc}x^2neq0\x-1neq0end{array}right rightarrow quad left[begin{array}{ccc}xneq0\xneq1end{array}right :text{ODZ}\\\frac{x^2(x^2-1)}{4x^2(x-1)}=0\\\frac{(x-1)(x+1)}{4(x-1)}=0\\\frac{x+1}{4}=0\\\x+1=0\\\boxed{x=-1}$