SOLUTION: Could you help me solve: 9x^4-21x^2+10=0

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Question 273250: Could you help me solve:
9x^4-21x^2+10=0
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
9x^4-21x^2+10=0

Let k = x^2

Equation becomes:

9k^2 - 21k + 10 = 0

This equations factors out to be:

(3k-5) * (3k-2) = 0

solve for k to get:

k = 5/3 or k = 2/3

Since we set k = x^2, then:

k = 5/3 is the same as x^2 = 5/3
k = 2/3 is the same as x^2 = 2/3

Solving for x, we get:

x = +/- sqrt%285%2F3%29
x = +/- sqrt%282%2F3%29

plug these into your original equation to see if they hold up.

your original equation is:

9x^4 - 21x^2 + 10 = 0

I plugged these values into that equation and they all proved to be true so the values are good.

For example:

When x = -sqrt%285%2F3%29, the equation becomes:

9%2A%28-sqrt%285%2F3%29%29%5E4+-+21%2A%28-sqrt%285%2F3%29%29%5E2+%2B+10+=+0 which becomes:

25 - 35 + 10 = 0 which becomes:

-10 + 10 = 0 which becomes:

0 = 0 confirming that the value of -sqrt%285%2F3%29 is good.

Your answers are:

x = plus or minus sqrt%285%2F3%29
and:

x = plus or minus sqrt%282%2F3%29