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jean143965
05.06.2020 •
Mathematics
What are the solutions of the equation x4 – 9x2 + 8 = 0? Use u substitution to solve. x = 1 and x = 2 StartRoot 2 EndRoot x = ±1 and x = plus-or-minus 2 StartRoot 2 EndRoot x = ±i and x = plus-or-minus 2 i StartRoot 2 EndRoot x = ±i and x = 2 StartRoot 2 EndRoot
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Ответ:
The solutions are
x = -1, 1, -2√2, and 2√2.
Step-by-step explanation:
Given the equation
x^4 - 9x² + 8 = 0
Let u = x², then the equation becomes
u² - 9u + 8 = 0
u² - u - 8u + 8 = 0
(u² - u) - (8u - 8u) = 0
u(u - 1) - 8(u - 1) = 0
(u - 8)(u - 1) = 0
u - 8 = 0
=> u = 8
Or
u - 1 = 0
=> u = 1
For u = 8
=> x² = 8
=> x = ±√8 = ±2√2
For u = 1
=> x² = 1
=> x = ±√1 = ± 1
Ответ:
Hope this helps!! ;))
Have a grat day!! <3