Question

[phan tuấn anh]

Tìm GTLN của B=\(\sqrt{x^2-6x+2y^2+4y+20}+\sqrt{x^2+2x+5}\)

Answer 1

[Nguyễn Văn Tiến]

toan violympic lop 9 la GTNN

\(B=\sqrt{x^2-6x+2y^2+4y+20}+\sqrt{x^2+2x+5}\)

\(=\sqrt{\left(x-3\right)^2+2\left(y+1\right)^2+9}+\sqrt{\left(x+1\right)^2+4}\ge\sqrt{9}+\sqrt{4}=5\)

tick nha

Answer 2

[Nguyễn Nhật Minh]

\(B=\sqrt{\left(3-x\right)^2+2\left(y+1\right)^2+3^2}+\sqrt{\left(x+2\right)^2+2^2}\ge\sqrt{\left(3-x+x+2\right)^2+\left(3+2\right)^2}=5\sqrt{2}\)

Bmin = \(5\sqrt{2}\) khi x=0 ; y =-1

B min nhé