Question

\(N=\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-1}-\dfrac{\sqrt{a}-1}{\sqrt{a}+1}+4\sqrt{a}\right)\left(\sqrt{a}+\dfrac{1}{\sqrt{a}}\right)\)

\(\left(a>0,a\ne1\right)\)

a) Rút Gọn N

b)Tính giá trị N khi \(a=29-12\sqrt{5}\)

Answer 1

a) \(\left(\dfrac{\sqrt{a}+1}{\sqrt{a}-1}-\dfrac{\sqrt{a}-1}{\sqrt{a}+1}+4\sqrt{a}\right)\left(\sqrt{a}+\dfrac{1}{\sqrt{a}}\right)\)

=\(\dfrac{\left(\sqrt{a}+1\right)^2-\left(\sqrt{a}-1\right)^2+4\sqrt{a}\left(a-1\right)}{a-1}.\dfrac{a+1}{\sqrt{a}}\)

=\(\dfrac{a+2\sqrt{a}+1-a+2\sqrt{a}-1+4a\sqrt{a}-4\sqrt{a}}{a-1}.\dfrac{a+1}{\sqrt{a}}\)

=\(\dfrac{4a\sqrt{a}}{a-1}.\dfrac{a+1}{\sqrt{a}}=\dfrac{4a\left(a+1\right)}{a-1}\)

b) tự thay