Question

What substitution should be used to rewrite x8 – 3x4 + 2 = 0 as a quadratic equation?

Answer 1

Answer:

The substitution is

$u = x ^ 4$

$u ^ 2 -3u +2 = 0$

Step-by-step explanation:

We have the 8th degree polynomial equation

$x ^ 8 - 3x^4 -+2 = 0$

To rewrite the equation as a quadratic function, take the common factor of the term x with the smallest exponent, in this case it is $x ^ 4$.

Now make a change of variable

$u = x ^ 4$.

So rewriting the equation in terms of u, we have:

$u ^ 2 -3u +2 = 0$

Now the initial equation became a quadratic equation

Factoring is left:

$(u-2) (u-1) = 0$

$u = 2$ and $u = 1$

$x ^ 4 = 2$ and $x ^ 4 = 1$

Answer 2

Answer:

substitution should be p =  x⁴

Step-by-step explanation:

It is given that,

x⁸ -  3x⁴ + 2 = 0

we can rewrite the equation,

(x⁴)² - 3x⁴ + 2 =0

To find the substitution

Here we can see that x⁴ is common in two terms of the given equation

we can substitute p instead of x⁴, the equation becomes,

p² - 3p +2 = 0

Therefore substitution should be used to rewrite x8 – 3x4 + 2 = 0 as a quadratic equation is p =  x⁴