Library / /100 of 860
Algebra Difficulty 4.8 AIME Find the answer
If x,y, and z are real numbers such that 2x2+y2+z2=2x−4y+2xz−5, find the maximum possible value of x−y+z.
A number or a short expression. Fractions can be typed as 3/2, and spacing doesn't matter.
Solution
The equation rearranges as (x−1)2+(y+2)2+(x−z)2=0, so we must have x=1, y=−2,z=1, giving us 4 .
Want a route through all this instead of an archive?
The track
puts 2,000 problems in a working order, from AMC 10 level to the IMO shortlist.
Source: Omni-MATH,
licensed Apache-2.0.
Statement and solution reproduced as published; topic and difficulty added by this site.