Question

Solve the equation by identifying the quadratic form. Use a substitute variable(t) and find all real solutions by factoring. Type your answers from smallest to largest. If an answer is not an integer then type it as a decimal rounded to the nearest hundredth. When typing exponents do not use spaces and use the carrot key ^ (press shift and 6). For example, x cubed can be typed as x^3.x^4-10x^2+9=0Step 1. Identify the quadratic formLet t= Answer. We now have:t^2-10t+9=0Step 2. FactorFactor this and solve for t to get t=Answerand Answer Step 3. Solve for xWe have solved for t now we need to use this value for t to help us solve for x. Revisit step 1 to remind you of the relationship between t and x. Type your answers from smallest to largest.x= +/-Answer and +/-Answer

Answer 1

As given by the question

There are given that the original equation is:

$x^4-10x^2+9=0$

Now,

Step 1:

Let,

$t=x^2$

Then,

Put the t instead of x

Then,

The equation becomes:

$\begin{gathered} x^4-10x^2+9=0 \\ t^2-10t^{}+9=0 \end{gathered}$

Step 2: Factor

From the equation

$\begin{gathered} t^2-10t^{}+9=0 \\ t^2-9t-t+9=0 \\ (t-9)(t-1)=0 \end{gathered}$

Then,

The value of t is,

$t=9,\text{ and t=1}$