SOLUTION: Hi so basically I need to simplify all square roots and answers should not be decimals Factor or solve the following: X⁴-16x²+48 I know this is a trinomial and that it might b

Algebra ->  Exponential-and-logarithmic-functions -> SOLUTION: Hi so basically I need to simplify all square roots and answers should not be decimals Factor or solve the following: X⁴-16x²+48 I know this is a trinomial and that it might b      Log On


   

Question 1174746: Hi so basically I need to simplify all square roots and answers should not be decimals Factor or solve the following:
X⁴-16x²+48
I know this is a trinomial and that it might be good to use the slide rule. Also I'm not sure if it needs to use the zero product property..
Anyway if you can help I will leave a great review!
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


+x%5E4+-+16x%5E2+%2B+48+ can be 'factored' but not 'solved' 



If you had

+u%5E2+-+16u+%2B+48+   you'd have +%28u-12%29%28u-4%29+  so let u=x%5E2 and you're mostly done:  +%28x%5E2-12%29%28x%5E2-4%29+ 



Factoring a 2nd time and simplifying, gives:

+%28x-2sqrt%283%29%29%28x%2B2sqrt%283%29%29%28x-2%29%28x%2B2%29+

Answer by ikleyn(52847) About Me  (Show Source):
You can put this solution on YOUR website!
.

Factor it as follows


    x^4 - 16x^2 + 48 = (x^2-12)*(x^2-4) = %28x-2%2Asqrt%283%29%29%2A%28x%2B2%2Asqrt%283%29%29%2A%28x-2%29%2A%28x%2B2%29.


The roots are  2sqrt%283%29, -2%2Asqrt%283%29, 2 and -2.


PLEASE STOP posting duplicates, triplicates, quadruplicates . . . and other . . . plicates . . .