Solve: -x^4 + 200 = 102x^2
I know the last line was wrong I just took a guess on factoring it out. I just knew how to do the first 2 lines. The problem has no typos it is -x, its crazy but that's how it is in my book. how does that change the answer?
"Your last line makes absolutely no sense.
Just multiply the first terms in each bracket all together, you would get x^6 !!! and your last term would be -520200" !!!
"Also I think you have a type.
If your equation is
+x^4 + 200 = 102x^2 it works out very nicely, so I am going to assume that the -x^4 is incorrect".
x^4 - 102x^2 + 200 = 0
(x^2 - 2)(x^2 - 100) = 0
so x = �}�ã2 or x = �}10
if it is indeed -x^4 + 200 = 102x^2 then
x^4 + 102x^2 - 200 = 0 gives you a "messy" solution.
it might be easier for you to see if I let y = x^2
then we have
y^2 + 102y - 200 = 0
and by the formula I got
y = (-102 ±√11204)/2
= 1.92447 or -103.92447
so x=√1.92477 = ±1.387
or x=√-103.92447 = ±10.194i
BTW, when you cut-and-pasted some of my previous reply, my square root symbols came out as �}�ã
Do you see an actual square root symbol in my post above?, I hope so.
To solve the equation -x^4 + 200 = 102x^2, let's first assume that there was a typo in the equation and the correct equation is actually x^4 - 102x^2 + 200 = 0.
To solve this quadratic equation, we can use factoring. We notice that the equation is in the form of a quadratic trinomial, so we want to find two binomials (a and b) that, when multiplied together, give us the original expression.
The factored form of the equation would be (x^2 - a)(x^2 - b) = 0. We want to find values for a and b such that when we expand this expression, we end up with x^4 - 102x^2 + 200.
By expanding (x^2 - a)(x^2 - b), we get x^4 - (a + b)x^2 + ab.
Comparing this with the original expression x^4 - 102x^2 + 200, we can see that a + b must be -102 and ab must be 200.
Now, we need to find two numbers whose sum is -102 and whose product is 200. These numbers are -2 and -100.
So, the factored form of the equation becomes (x^2 - 2)(x^2 - 100) = 0.
Now, we can set each factor equal to zero and solve for x:
x^2 - 2 = 0 gives us x = ±√2
x^2 - 100 = 0 gives us x = ±10
Therefore, the solutions to the equation x^4 - 102x^2 + 200 = 0 are x = ±√2 and x = ±10.