Question

1. to solve the equation $4m^4 - 3 = m^2 + 2$, what substitution would we make to convert it to a quadratic equation?

$n = \square$

Explanation:

Step1: Identify the form

The equation is \(4m^4 - 3 = m^2 + 2\). Notice that \(m^4=(m^2)^2\).

Step2: Choose substitution

Let \(n = m^2\). Then \(m^4=n^2\), and the equation becomes \(4n^2 - 3 = n + 2\), which is a quadratic in \(n\).

Answer:

\(m^2\) (or \(n = m^2\))