Question

aratati ca numarul n=5√11 -5√3+√75-4√11- 11 pe √11 este nr intreg

Answer 1

5√11-5√3+√75-4√11-11/√11=5√11-4√11-11/√11 -5√3+√25*3=
√11-11/√11-5√3+5√3=√11-11/√11

(√11)  / √11-11/√11=  11-11√11/√11= 11-11=0

Answer 2

$\it \ n =5\sqrt{11} -5\sqrt3+\sqrt{75} -4\sqrt{11} -\dfrac{11}{\sqrt{11}}$

$\it \sqrt{75} =\sqrt{25\cdot3}=5\sqrt3$

$\it \dfrac{11}{\sqrt{11}} =\dfrac{\sqrt{11}\cdot \sqrt{11}}{\sqrt{11}} =\sqrt{11}$

$\it -4\sqrt{11} -\sqrt{11} = -5\sqrt{11}$

$\it n =5\sqrt{11} -5\sqrt3+5\sqrt3-5\sqrt{11} \Longrightarrow\ n = 0 \in \mathbb{Z}$