Question

已知实数x.y满足3x-4y+5=0,求（x-2)的平方+(y+1)的平方的最小值

Answer 1

3x-4y+5=0

3x-6=4y-11

3(x-2)=4y-11

x-2=(4y-11)/3

（x-2)的平方+(y+1)的平方

=(4y-11)^2/9+(y+1)^2

=(16y^2-88y+121)/9+y^2+2y+1

=(25/9)y^2-70/9 y+130/9

=25/9(y^2-14/5 y)+130/9

=25/9(y-7/5)^2-25/9*49/25+130/9

=25/9(y-7/5)^2+9

即当y=7/5时,最小值是+9.

此时x=1/5