Question

Решите уравнения:
4x^2-x^4=0
5x^4-125x^2=0
3x^4+27x^2=0

Answer 1

$4 {x}^{2} - 4 {x}^{4} = 0 \ 4x times (1 - {x}^{2} ) = 0 \ x times (1 - {x}^{2} ) = 0 \ 1){x}^{2} = 0 \ 2)1 - {x}^{2} = 0$

Отсюда: х¹ = 0, х² = -1, х³ = 1.

$5 {x}^{4} - 125 {x}^{2} = 0 \ 5 {x}^{2} times ( {x}^{2} - 25) = 0 \ {x}^{2} times ( {x}^{2} - 25) = 0 \ 1) {x}^{2} = 0 \ 2) {x}^{2} - 25 = 0$

Отсюда: х¹ = 0, х² = 5, х³ = -5.

$3 {x}^{4} + 27 {x}^{2} = 0 \ 3 {x}^{2} times ( {x}^{2} + 9) = 0 \ {x}^{2} times ( {x}^{2} + 9) = 0 \ 1) {x}^{2} = 0 \ 2) {x}^{2} + 9 = 0$

Отсюда: х¹ = 0.