Question

What are the solutions of the equation x4 6x2 5 = 0? use u substitution to solve.

Answer 1

The value of the x from the given equation is a +i and -i and +5i and -5i.

According to the statement

we have given that the equation $x^4 + 6x^2 +5 =0$

and we have to find the value of x by the u substitution.

So,

The given equation is

$x^4 + 6x^2 +5 =0$

Put $x^2 = u$ 

By substitution method

Then the equation become

$u^2 +6u +5 = 0$

And solve the equation then

$u^2+ u +5u +5 = 0$

Then

u(u +1) + 5(u +1) = 0

(u+5) (u +1) = 0

Then

the value of u is -1 and -5 then

The value of x is

$x = \sqrt{u}$

x = √-5 And √-1

Then the value of x is +i and -i and +5i and -5i.

So, The value of the x from the given equation is a +i and -i and +5i and -5i.

Learn more about substitution method here

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