x ^ 4 + 2 x ^ 2 - 15 = 0
Substitute :
u = x ^ 2
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Remark :
If u = x ^ 2 then x ^ 4 = u ^ 2
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You must solve equation :
u ^ 2 + 2 u - 15 = 0
The exact solutions are :
u = 3
and
u = - 5
So solutions are :
x ^ 2 = 3
x = sqrt ( 3 )
x = - sqrt ( 3 )
x ^ 2 = - 5
x = sqrt ( - 5 ) = i sqrt ( 5 )
x = - sqrt ( - 5 ) = - i sqrt ( 5 )
Equation :
x ^ 4 + 2 x ^ 2 - 15 = 0
has 4 solutions ( 2 real and 2 imaginary )
P.S.
If you don't know how to solve equation :
u ^ 2 + 2 u - 15 = 0
In google type:
quadratic equation online
When you see list of results click on:
Free Online Quadratic Equation Solver:Solve by Quadratic Formula
When page be open in rectangle type:
u ^ 2 + 2 u - 15 = 0
and click option: solve it
You will see solution step-by step
How many solutions equation x^4 + 2x^2 - 15 = 0 has?
1 answer