Question

Let m=x^2.
Which equation is equivalent to (x^2-5)^2-3x^2+15=-2.

Answer 1

Answer: m² - 13m + 42 = 0

Explanation:

Given m = x²

Then original equation

( x² - 5 )² - 3x² + 15 = -2

Now replace x² by m

( m - 5 )² - 3m + 15 = -2

Now considering ( m - 5 )² , we can open or expand the expression and later simplify. Therefore

( m - 5 )² = m² -10m + 25

Now put this in the above expression and simplify.

( m- 5 )² - 3m + 15 = -2 ,now becomes

(m² - 10m + 25) - 3m + 15 = -2

m² - 10m -3m + 25 + 15 + 2 = 0

m² - 13m + 42 = 0

Answer 2

Answer:
`m^2 - 13m + 38 = 0`

Explanation:

`m = x^2\\(x^2-5)^2-3x^2+15=-2.`

We can go simplify the equation by simplifying the first polynomial:

`(x^2-5)^2 = x^4 - 10x^2+25`

Then, we can substitute that in the original equation:

`x^4 - 13x^2 + 38 = 0`

Now, we can substitute m for every x^2.

Knowing that x^4 = x^2 * x^2, we can write this as m^2:

`m^2 - 13m + 38 = 0`