Posted by **Justin** on Thursday, March 29, 2007 at 1:42pm.

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).

Can you please help me understand where the -3x^2 came from?

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.

## Answer This Question

## Related Questions

- Algebra 2: Radicals URGENT!! - Could some kind, saintly soul help me solve this ...
- math - how would you simplify this equation: y = (x+3)/[(4-sqrt(16+h))] please ...
- Math - How do you find a square root of a number that's not a perfect square? I'...
- Math/Calculus #2 - Integrate: 1/(x-sqrt(x+2) dx I came up with: (2/3)(2*ln((sqrt...
- Calculus - Please look at my work below: Solve the initial-value problem. y'' + ...
- MATH PLEASE CHECK IT!!2 - sqrt2/sqrt10 here is what I got: sqrt (2/10)= sqrt (1/...
- math calculus please help! - l = lim as x approaches 0 of x/(the square root of...
- radical equation please help!!! - sqrt(1+x) -sqrt(1-x) = sqrt (1-x-sqrt(1+x)) ...
- algebra,math,help - Use Property 2 to simplify each of the following radical ...
- Math Help please!! - Could someone show me how to solve these problems step by ...

More Related Questions