Решите н, биквадратное уравнение! x⁴-5x²-36=0 y⁴-6y²+8=0 t⁴=10t²+25=0 4x⁴-5x²+1=0 9x⁴-9x²+2=0 16y⁴-8y²+1=0

1) x⁴ - 5x² - 36 = 0;

t = x².

t² - 5t - 36 = 0;

t = 9; t = - 4;

x₁ = - 3; x₂ = 3; x ∉ R.

2) y⁴ - 6y² + 8 = 0;

t² - 6t + 8 = 0;

t = 4; t = 2;

y₁ = - 2; y₂ = 2; y₃ = - √2; y₄ = √2.

3) t⁴ - 10t² + 25 = 0;

(t² - 5) ² = 0;

t₁ = - √5, t₂ = √5.

4) 4x⁴ - 5x² + 1 = 0;

4t² - 5t + 1 = 0;

t = 1; t = 1/4;

x₁ = - 1; x₂ = 1; x₃ = - 1/2; x₄ = 1/2;

5) 9x⁴ - 9x² + 2 = 0;

9t² - 9t + 2 = 0;

t = 2/3; t = 1/3;

x₁ = - √6/3; x₂ = √6/3; x₃ = - √3/3; x₄ = √3/3.

6) 16y⁴ - 8y² + 1 = 0;

(4y² - 1) ² = 0;

y₁ = 1/2; y2 = - 1/2.