Question

tìm gtln

a) \(B=1-\sqrt{x^2-2x+2}\)

b) \(C=1+\sqrt{4x-x^2-2}\)

Answer 1

a: \(B=1-\sqrt{\left(x-1\right)^2+1}\)

(x-1)^2+1>=1

=>\(\sqrt{\left(x-1\right)^2+1}>=1\)

=>\(B< =0\)

Dấu = xảy ra khi x=1

b: 

ĐKXĐ: -(x+2)^2+2>=0

=>-(x+2)^2>=2

=>(x+2)^2<=2

=>\(-\sqrt{2}-2< =x< =\sqrt{2}-2\)

\(-x^2+4x-2=-\left(x^2-4x+2\right)\)

\(=-\left(x^2-4x+4-2\right)=-\left(x-2\right)^2+2< =2\)

=>\(0< =\sqrt{4x-x^2-2}< =\sqrt{2}\)

=>1<=C<=căn 2+1

\(C_{max}=\sqrt{2}+1\Leftrightarrow x=2\)