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What are the soultions of the equation x^4 - 9x^2 + 8 = 0? Use u substitution to solve.​

User Gwk
by
8.1k points

1 Answer

9 votes

Explanation:

Let u=x^2.

Notice that


{x}^(4) - 9 {x}^(2) + 8 = 0


( {x}^(2) ) {}^(2) - 9( {x}^(2) ) + 8 = 0


u {}^(2) - 9u + 8 = 0


(u - 8)(u - 1) = 0


u = 8


u = 1

Replace x^2= u


{x}^(2) = 8


x = ±2 √(2)


{x}^(2) = 1


x = ±1

So our answer is


±1 \:

and


±2 √(2)

User Malk
by
7.8k points

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