Question

X^4-10x^2+9=0........

Answer 1

Ответ:

Пошаговое объяснение:

x^4-10x^2+9=0     Биквадратное уравнение

x^2 = t     t≥0

t^2-10t+9=0

По t.Vieta:

t₁ = 9

t₂ = 1

Обратная замена:

x²=9

x= 3 ; -3

x²=1

x= 1 ; -1

Answer 2

To solve the equation x^4 - 10x^2 + 9 = 0, we can use a substitution to simplify the equation. Let's substitute a new variable, such as y, where y = x^2.

Substituting y into the equation, we get y^2 - 10y + 9 = 0. Now, we can solve this quadratic equation for y.

Factoring the quadratic equation, we have (y - 1)(y - 9) = 0.

Setting each factor equal to zero, we have two possible solutions: y - 1 = 0 and y - 9 = 0.

For y - 1 = 0, we have y = 1.

For y - 9 = 0, we have y = 9.

Now, substitute y back into the original equation, y = x^2.

For y = 1, we have x^2 = 1. Taking the square root of both sides, we have x = ±1.

For y = 9, we have x^2 = 9. Taking the square root of both sides, we have x = ±3.

Therefore, the solutions to the equation x^4 - 10x^2 + 9 = 0 are x = ±1 and x = ±3.