Question

cho biểu thức P = \(\left(\dfrac{1-a\sqrt{a}}{1-\sqrt{a}}+\sqrt{a}\right).\left(\dfrac{1+a\sqrt{a}}{1+\sqrt{a}}-\sqrt{a}\right)\)

a, rút gọn P

b, tìm a để P < 7−4√3

Answer 1

`a)P=((1-asqrta)/(1-sqrta)+sqrta).((1+asqrta)/(1+sqrta)-sqrta)`

`=(((1-sqrta)(a+sqrta+1))/(1-sqrta)+sqrta).(((1+sqrta)(a-sqrta+1))/(1+sqrta)-sqrta)`

`=(a+sqrta+1+sqrta)(a-sqrta+1-sqrta)`

`=(a+2sqrta+1)(a-2sqrta+1)`

`=(sqrta+1)^2(sqrta-1)^2`

`=(a-1)^2`

`b)a<7-4sqrt3`

`<=>(a-1)^2<(2-sqrt3)^2`

`<=>sqrt3-2<a-1<2-sqrt3`

`<=>sqrt3-1<a<3-sqrt3`