Question

X⁴ - 5x² + 4 = 0 ........................​

Answer 1

x⁴ - 5x² + 4 = 0

Сделаем замену : x² = m , m ≥ 0

m² - 5m + 4 = 0

По теореме Виета :

m₁ = 1      m₂ = 4

1) x² = 1

x₁ = 1     x₂ = - 1

2) x² = 4

x₃ = 2    x₄ = - 2

Ответ : 1 ; - 1 ; 2 ; - 2

Answer 2

Воспользуемся методом замены:

t=x²

Тогда:

t²-5t+4=0

D=b²-4ac = 25-16 = 9, D>0 - 2 различных корня

$t1 = \frac{-b+\sqrt{D} }{2a} = \frac{5+3}{2} = 4\\t2 = \frac{-b-\sqrt{D} }{2a} = \frac{5-3}{2} = 1$

Подставим найденные значения t:

x² = 4                      x² = 1

x = ± 2                     x = ± 1

Ответ: {-2; -1; 1; 2}

Answer 3

To solve the equation X⁴ - 5x² + 4 = 0, we can use a substitution technique to simplify the equation. Let's substitute a variable, say "y," for x². The equation becomes:

y² - 5y + 4 = 0

Now we can solve this quadratic equation by factoring or using the quadratic formula. Let's factor it:

(y - 4)(y - 1) = 0

Now we have two possible values for y:

1. y - 4 = 0 y = 4

2. y - 1 = 0 y = 1

Since y represents x², we can solve for x by taking the square root of each value of y:

1. For y = 4: x² = 4 x = ±2

2. For y = 1: x² = 1 x = ±1

So the solutions to the equation X⁴ - 5x² + 4 = 0 are x = ±2 and x = ±1.