Question

Cho bthuc P = \(\left(1+\dfrac{a+\sqrt{a}}{\sqrt{a}-1}\right)\).\(\left(1-\dfrac{a-\sqrt{a}}{\sqrt{a}-1}\right)\)

a) Rút gọn P

b) Tìm a để P > -\(\sqrt{2}\)

c) Tìm a để P=\(\sqrt{a}\)

Answer 1

a: Sửa đề: \(P=\left(1+\dfrac{a+\sqrt{a}}{\sqrt{a}+1}\right)\left(1-\dfrac{a-\sqrt{a}}{\sqrt{a}-1}\right)\)

\(=\left(1+\sqrt{a}\right)\left(1-\sqrt{a}\right)\)

=1-a

b: Để P>-căn 2 thì \(1-a>-\sqrt{2}\)

=>\(-\sqrt{a}>-\sqrt{2}-1\)

=>\(\sqrt{a}< \sqrt{2}+1\)

=>\(0< =a< 3+2\sqrt{2}\)

c: Để P=căn a thì \(1-a-\sqrt{a}=0\)

=>\(\sqrt{a}=\dfrac{-1+\sqrt{5}}{2}\)

hay \(a=\dfrac{6-2\sqrt{5}}{4}=\dfrac{\sqrt{5}-1}{2}\)