Exponents Problem Assistance

[DrPepper]

Solve

I am not looking for someone to give me the answer to this problem, but I would really appreciate some assistance in helping me understand HOW to solve this type of problem. I want to know how so that I can be prepared for my test. Thank you

 

[pka]

Solve
View attachment 1699

HINT: \(\displaystyle 9\cdot 80=720\)

 

[Deleted member 4993]

Solve
View attachment 1699
I am not looking for someone to give me the answer to this problem, but I would really appreciate some assistance in helping me understand HOW to solve this type of problem. I want to know how so that I can be prepared for my test. Thank you

substitute:

u = x²

then you'll see a quadratic equation...

 

[pka]

Thank you for your reply...I'm sorry, but I'm a bit confused.

Write the equation as \(\displaystyle x^4-89x^2+720=0~.\)

Using reply #4 you can simplify to:
\(\displaystyle u^2-89u+720=0~.\)

 

[DrPepper]

u^2 -89u+720
factors into (u - 9) (u - 80)

 

[pka]

u^2 -89u+720
factors into (u - 9) (u - 80)

So \(\displaystyle u=9\text{ or }80.\)

Now let \(\displaystyle x^2=u.\)

 

[DrPepper]

So I get 3 and 4 sqrt(5)

 

[pka]

So I get 3 and 4 sqrt(5)

Well, not complete.

\(\displaystyle x=\pm3\text{ or }\pm4\sqrt5\)

 

[DrPepper]

Thank you kindly for your assistance...this makes much more sense to me now!