SOLUTION: Find the real solution. {{{x^4-10x^2+25=0}}}

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Question 5219: Find the real solution.
x%5E4-10x%5E2%2B25=0
Found 2 solutions by rapaljer, ichudov:
Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
This one factors like a trinomial:
x%5E4-10x%5E2%2B25=0
%28x%5E2+-+5%29%28x%5E2+-+5%29+=+0+ or +%28x%5E2+-+5%29%5E2+=+0+

So, x%5E2+-+5+=+0

Add + 5 to each side of this equation:
x%5E2+-+5+%2B+5+=+5
x%5E2+=+5

Take square root of each side of the equation. (DON'T FORGET THE + or - !!)
+x+=+sqrt+%285%29+ or x+=+-+sqrt+%285%29

R^2 at SCC

Answer by ichudov(507) About Me  (Show Source):
You can put this solution on YOUR website!
This is a typical school problem with fourth and second degree in a trinomial. They are all solved the same way.
Use y instead of x%5E2. x%5E4 is y%5E2.
y%5E2-10y%2B25=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ay%5E2%2Bby%2Bc=0 (in our case 1y%5E2%2B-10y%2B25+=+0) has the following solutons:

y%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-10%29%5E2-4%2A1%2A25=0.

Discriminant d=0 is zero! That means that there is only one solution: y+=+%28-%28-10%29%29%2F2%5C1.
Expression can be factored: 1y%5E2%2B-10y%2B25+=+1%28y-5%29%2A%28y-5%29

Again, the answer is: 5, 5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-10%2Ax%2B25+%29


As you can see, the only solution is y=5, or x%5E2=5. So, x is either sqrt%285%29, or sqrt%28-5%29