# Math

posted by .

I have a problem that states to simplify.

The equation is d=sqrt(x^2+(4-x^2-2)^2)
The book tells me that the answer simplifies to sqrt(x^4-3x^2+4).

Thanks!

d=√(x^2 + (4 - x^2 - 2)^2)
=√(x^2 + (2 - x^2)^2)
=√(x^2 + x^4 - 4x^2 + 4)
=√(x^4 - 3x^2 + 4)

In my opinion, this is not much of a "simplification" problem

(4-x^2-2)^2 = (2 - x^2)^2 = x^4 - 4x^2 + 4
When you add the x^2 to that, you get
x^4 - 3x^2 + 4

(4 - x^2 - 2)^2 simplifies to (2 - x^2)^2. Expanding it gives x^4 - 2x^2 - 2x^2 + 4 = x^4 - 4x^4 + 4. Then you have that x^2 out in front that you can work with. so x^4 + x^2 - 4x^2 + 4 = x^4 - 3x^2 + 4.

## Similar Questions

1. ### math

how would you simplify this equation: y = (x+3)/[(4-sqrt(16+h))] please help me! you have three variables. I am not certain "simplify" is an appropriate term here. ohhhh it was my mistake. I meant: y = h/[(4-sqrt(16+h))] y = h/[(4-sqrt(16+h))] …

l = lim as x approaches 0 of x/(the square root of (1+x) - the square root of (1-x) decide whether: l=-1 or l=0 or l=1 Let me make sure I understand the question. Do we have lim x->0 x/[sqrt(1+x) - sqrt(1-x)] ?
3. ### MATH PLEASE CHECK IT!!2

sqrt2/sqrt10 here is what I got: sqrt (2/10)= sqrt (1/5) sqrt 0.2 * I don't think that it is right but pleasee check it.Thanks Yes, that is one way you could do it, then simplify further by taking the square root of 0.2, but you are …
4. ### Math

How do you find a square root of a number that's not a perfect square?
5. ### algebra,math,help

Use Property 2 to simplify each of the following radical expressions. sqrt (10)/ sqrt(49) My answer: sqrt (10) / (7) THis next one i need help: Use the properties for radicals to simplify each of the following expressions. Assume that …
6. ### Algebra 2: Radicals URGENT!!

Could some kind, saintly soul help me solve this problem?
7. ### Math/Calculus #2

Integrate: 1/(x-sqrt(x+2) dx I came up with: (2/3)(2*ln((sqrt(x+2))-2)+ln((sqrt(x+2))-1)) but it keeps coming back the wrong answer even though I integrated correctly. Is there a way to simplify this answer, and if so, how?
8. ### Calculus

Please look at my work below: Solve the initial-value problem. y'' + 4y' + 6y = 0 , y(0) = 2 , y'(0) = 4 r^2+4r+6=0, r=(16 +/- Sqrt(4^2-4(1)(6)))/2(1) r=(16 +/- Sqrt(-8)) r=8 +/- Sqrt(2)*i, alpha=8, Beta=Sqrt(2) y(0)=2, e^(8*0)*(c1*cos(0)+c2*sin(0))=c2=2 …