a:ĐKXĐ: a>0; a<>1
\(P=\left(\frac{1}{1-\sqrt{a}}-\frac{1}{1+\sqrt{a}}\right)\left(\frac{1}{\sqrt{a}}+1\right)\)
\(=\frac{1+\sqrt{a}-1+\sqrt{a}}{\left(1-\sqrt{a}\right)\left(1+\sqrt{a}\right)}\cdot\frac{1+\sqrt{a}}{\sqrt{a}}=\frac{2\sqrt{a}}{\sqrt{a}\left(1-\sqrt{a}\right)}=\frac{2}{1-\sqrt{a}}\)
b: P>1/2
=>\(P-\frac12>0\)
=>\(\frac{2}{1-\sqrt{a}}-\frac12>0\)
=>\(\frac{4-1+\sqrt{a}}{2\left(1-\sqrt{a}\right)}>0\)
=>\(\frac{\sqrt{a}+3}{2\left(1-\sqrt{a}\right)}>0\)
=>\(1-\sqrt{a}>0\)
=>\(\sqrt{a}<1\)
=>0<a<1
Đúng 0
Bình luận (0)
