` A(x) = (x-4)^2 + 2020`
`B(x) = 4|x-4| -4`
` M(x) = A(x) - B(x) -14 = (x-4)^2 +2020 - ( 4|x-4| -4 ) -14`
` = (x-4)^2 + 2020 - 4|x-4| +4 -14`
` = (x-4)^2 - 4|x-4| + 4 + 2006`
` = (x-4)^2 - 2|x-4| - 2|x-4| +4 + 2006`
` = |x-4|(|x-4| -2) - 2 (|x-4| -2) + 2006`
` = ( |x-4| -2 ) (|x-4| -2 ) + 2006`
` = ( |x-4| -2 )^2 +2006`
Ta có ` ( |x-4| -2 )^2 \ge 0` nên ` ( |x-4| -2 )^2 +2006 \ge 2006`
`\to` GTNN ` M(X) = 2006`;
Dấu `=` xảy ra khi ` |x-4| -2 = 0 \to |x-4| = 2`
`\to x -4 = 2` hoặc ` x-4 = -2`
`\to x = 6` hoặc ` x = 2`
Vậy min `M_(x) = 2006` khi ` x= 6` hoặc ` x= 2`
