(xn+2-1)/(x2-1)
Explanation
Let Y=1+x2+x4+...+xn. Now notice that:
Y=1+x2+x4+...+xn=x2(1+x2+x4+...+xn-2)+1
Y+xn+2=x2(1+x2+x4+...+xn-2+xn)+1
Y+xn+2=x2*Y+1
Y+xn+2-x2*Y=1
Y-x2*Y=1-xn+2
Y(1-x2)=1-xn+2
Y=(1-xn+2)/(1-x2)=(xn+2-1)/(x2-1)
x2 + x2 = 2x2
x2 + x2 = 2x2
x2 + 36 cannot be factored. You can only factor the difference of two squares, not the sum.
x4 +x2 =x2 (x2+1)
This quadratic equation has no real roots because its discriminant is less than zero.
(xn+2-1)/(x2-1)
3x2 + 2x + 3 + x2 + x + 1 = 4x 2+ 3x + 4
4x2 -x -1 :D
-3/2
(x + 3)2 = (x + 2)2 + 9 x2 + 6x + 9 = x2 + 4x + 4 + 9 2x = 4 x = 2
x2 + x2 + x2 = (1 + 1 + 1)x2 = 3x2
x2 + 4x - 21 = (x + 7)(x - 3). The trick is to find 2 numbers which sum to 4 and have a product of -21.
x2 + x2 = 2x2
3x4 plus 5x3 plus x2 - 5 divided by x 2 =[(3x4) + (5x3) + (x2 - 5)]/x2 =(12 + 15 + x2 -5)/x2 =(27 - 5 + x2)/x2 =(22 + x2)/x2
x2 + 48x + 320
x2 + x2 = 2x2
x2 + 36 cannot be factored. You can only factor the difference of two squares, not the sum.