Completing the square
By Hal 2001 on Monday, September 17, 2001
- 04:51 pm:
How do you go about completing the square for the
following?
i) sin2 x + 4sinx, and
ii) x4 + 2x2 + y4 -
2y2 + 3
Thanks for your help in advance.
By Olof Sisask on Monday, September 17,
2001 - 08:17 pm:
Hi Hal,
For (i), let y=sinx, then your equation
=y2+4y=(y+2)2-4
(ii)
=(x2+1)2-1+(y2-1)2-1+3=(x2+1)2+(y2-1)2+1
If this is equal to 0, then there are no real solutions for x and y, since
(x2+1)2 ³ 0 and (y2-1)2 ³ 0.
In general, if you have x2+a x+b, then completing the square gives
(x+a/2)2-a2/4+b.
Regards,
Olof