Solve: x^4 - 34x^2 = -225?

Question

a) no solution
b) 3,-5
c) 3,-3,5,-5
d) 3,-3



explain how to do it .

Answer 1

The most sure fire way to solve this (other than just plugging numbers in and seeing what works), is to solve it with the quadratic formula via substitution.

Set x^2 = s

s^2 - 34s + 225 = 0

With the quadratic formula:

[34+-sqrt(1156 - 4(1)(225))] /2
=[34+-sqrt(256)]/2
=[34+-16]/2
= 9, 25

So s = 9 or 25
So x^2 = 9 or 25
So x = 3,-3, 5, -5

Answer 2

Note: x^4 - 34^2 = - 225 Make equal to zero
x^4 - 34x^2 + 225 = 0
(x^2)^2 - 34x^2 + 225 = 0 Need two numbers whose product = 225 and sum = -34
(x^2 - 9)(x^2 - 25) = 0 differences of squares
(x + 3)(x - 3)(x + 5)(x - 5) = 0
so x = +/- 3 and +/-5

Answer 3

C

Moving the 225 over gives x^2-34x^2+225

You can factor this as (x^2-9)(x^2-25)

Then you can factor these further as (x+3)(x-3)(x+5)(x-5)

Answer 4

x^4 - 34x^2 = -225
x^4 - 34x^2 + 225 = 0
(x+5)(x-5)(x+3)(x-3) = 0
x = - 5. . x = 5 . . . x = - 3... and . . . x = 3

Answer 5

x^2 = u

u^2 - 34u + 225 = 0

[ 34 +/- sqrt (34^2 - 900) ] / 2 = u
[ 34 +/- 16 ] / 2 = x^2
25 = x^2 or 9 = x^2
x = ±5 , ±3

Answer 6

use synthetic division. add 225 to the left side of the equation. then use synthetic division, it's the easiest way. because the number is 225, try numbers you know are divisible by it - like five. or because it's one of the choices, try that. n after that do another synthetic division using three because it's the other choice. and you should get a simple x squared and you can factor that out. once you solve for x, plug it back into the original equation n see if it's true.

if it is, then those are the solutions. it's c by the way.

Answer 7

x^4-34x^2+225=0 c.

(x^2-25)(x^2-9)=0
(x-5)(x+5)(x-3)(x+3)=0

x= 3,-3,5,-5