Question

So sánh: \(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\)và \(\sqrt{3}\)

Làm ơn giúp mình rồi mình like cho

Answer 1

Giả sử \(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\)\(\le\sqrt{3}\)

<=> 4 + \(\sqrt{7}\)+ 4 - \(\sqrt{7}\)- 2×\(\sqrt{16-7}\)\(\le3\)

<=> 8 - 6 \(\le3\)

<=> 2 \(\le3\)(đúng)

Vậy \(\sqrt{4+\sqrt{7}}-\sqrt{4-\sqrt{7}}\)< √3

Answer 2

\(\sqrt{4+7}-\sqrt{4-\sqrt{7}}=2,152902878\)

\(\sqrt{3}=1,732050808\)

Rùi so sánh đi