Question

so sánh :

a) x = \(\sqrt{961}-\left(\dfrac{1}{\sqrt{6}}-1\right)\) và y =\(\sqrt{1089}-\left(\dfrac{1}{\sqrt{7}}+1\right)\)

Answer 1

Ta có : \(\sqrt{961}< \sqrt{1089}\)

\(\left(\dfrac{1}{\sqrt{6}}-1\right)< \left(\dfrac{1}{\sqrt{7}}+1\right)\)

=> x<y

Goodluck

Answer 2

Ta có:

+) \(\sqrt{961}-\left(\dfrac{1}{\sqrt{6}}-1\right)\)

\(=31-\dfrac{1}{\sqrt{6}}+1\)

\(=32-\dfrac{1}{\sqrt{6}}\)

+)\(\sqrt{1089}-\left(\dfrac{1}{\sqrt{7}}+1\right)\)

\(=33-\dfrac{1}{\sqrt{7}}-1\)

\(=32-\dfrac{1}{\sqrt{7}}\)

* Ta lại có:

\(\sqrt{6}< \sqrt{7}\)

\(\Rightarrow\dfrac{1}{\sqrt{6}}>\dfrac{1}{\sqrt{7}}\)

\(\Rightarrow32-\dfrac{1}{\sqrt{6}}< 32-\dfrac{1}{\sqrt{7}}\) hay \(\sqrt{961}-\left(\dfrac{1}{\sqrt{6}}-1\right)< \text{​​}\text{​​}\) \(\sqrt{1089}-\left(\dfrac{1}{\sqrt{7}}+1\right)\)

Vậy \(\sqrt{961}-\left(\dfrac{1}{\sqrt{6}}-1\right)< \text{​​}\text{​​}\) \(\sqrt{1089}-\left(\dfrac{1}{\sqrt{7}}+1\right)\)

Bài này tớ giải bừa thoi, tớ đọc lại cũng thấy khó hiểu nữa mà