1) x⁴ - 24x² - 25 = 0
Пусть x² = t, t > 0
Тогда:
t² - 24t - 25 = 0
D = 24² - 4*(-25) = 676 = 26²
t₁ = (24 + 26)/2 = 50/2 = 25
t₂ = (24 - 26)/2 = -2/2 = -1 -- не удовл.
x² = 25
x = +- 5
Ответ: +-5.
2) x⁴ - 7x² + 10 = 0
Пусть x² = t, t > 0.
t² - 7t + 10 = 0
D = 7² - 4*10 = 49 - 40 = 9 = 3²
t₁ = (7 + 3)/2 = 10/2 = 5
t₂ = (7 - 3)/2 = 4/2 = 2
x² = 5
x = +-√5
x² = 2
x = +-√2
Ответ: +-√5; +-√2.
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1) x⁴ - 24x² - 25 = 0
Пусть x² = t, t > 0
Тогда:
t² - 24t - 25 = 0
D = 24² - 4*(-25) = 676 = 26²
t₁ = (24 + 26)/2 = 50/2 = 25
t₂ = (24 - 26)/2 = -2/2 = -1 -- не удовл.
x² = 25
x = +- 5
Ответ: +-5.
2) x⁴ - 7x² + 10 = 0
Пусть x² = t, t > 0.
Тогда:
t² - 7t + 10 = 0
D = 7² - 4*10 = 49 - 40 = 9 = 3²
t₁ = (7 + 3)/2 = 10/2 = 5
t₂ = (7 - 3)/2 = 4/2 = 2
x² = 5
x = +-√5
x² = 2
x = +-√2
Ответ: +-√5; +-√2.