Question

So sánh \(\dfrac{\sqrt{a}-1}{\sqrt{a}}\)với 1

Answer 1

ta có :

\(\sqrt{a}-1< \sqrt{a}\) (1)

mà : \(\dfrac{\sqrt{a}}{\sqrt{a}}=1\)

từ (1) suy ra : \(\dfrac{\sqrt{a}-1}{\sqrt{a}}< 1\)

kiến thức cấp I : ta có phân số \(\dfrac{a}{b}\) thì :

\(\dfrac{a}{b}\) < 1 nếu a < b ( VD : \(\dfrac{3}{4}\) < 1 )

\(\dfrac{a}{b}\) = 1 nếu a = b ( VD : \(\dfrac{4}{4}\) = 1)

\(\dfrac{a}{b}\) > 1 nếu a > b ( VD : \(\dfrac{5}{4}\) > 1 )

Answer 2

ta có\(\dfrac{\sqrt{a}+1}{\sqrt{a}}=\dfrac{\sqrt{a}}{\sqrt{a}}+\dfrac{1}{\sqrt{a}}\) =\(1+\dfrac{1}{\sqrt{a}}\)

suy ra 1+\(\dfrac{1}{\sqrt{a}}\)>1

hay \(\dfrac{\sqrt{a}+1}{\sqrt{a}}\)>1