Question

cho P=\(\dfrac{1}{2\left(1+\sqrt{a}\right)}+\dfrac{1}{2\left(1-\sqrt{a}\right)}-\dfrac{a^2+2}{1-a^3}\) với a\(\ge0,a\ne1\)

a) rút gọn P

b)tìm gtnn của P

Answer 1

a)

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

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

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

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

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

P =