91.3k views
3 votes
How do you solve this?

How do you solve this?-example-1

2 Answers

2 votes
x⁴-13x²+36
(x²-4)(x²-9)



x²=4. | x²=9
x=√4. |x=√9
x=2. |x=3




27x³-8=0
x³=8/27
x=2/3





...






















-------------------
User FabLouis
by
7.4k points
5 votes

Solve\ x^4-13x^2=-36.


View this equation as a quadratic like so:

x^2(x^2)-13x(x)+36=0

We can factor just like a normal quadartic!
We want two numbers that multiply to 36x² and add to -13x.
These numbers are -9x and -4x.
Because our leading coefficient is 1, we can factor straight to (x²-4)(x²-9).
Here's what it would look like if we split the middle and factored:

x^4-9x^2-4x^2+36=0\\x^2(x^2-9)-4(x^2-9)=0\\(x^2-4)(x^2-9)=0

Of course, any value which causes either factor to equal zero is a solution.
The other factor times zero is still going to be zero, of course.
Let's derive these two possibilities from our equation.

x^2-4=0,\ or\ x^2-9=0
We can add that constant to the right side...

x^2=4,\ or\ x^2=9
And take the square root of each side.

\boxed{x=\pm2\ or\ \pm3}

So, your possible x values are
2, -2, 3, and -3.
User Yannick Schall
by
7.7k points