Question

Rezolvati in multimea numerelor naturale :
$( \sqrt{3} -x) ^{2} - \sqrt{3} ( \sqrt{12} -3)<11+(x-2 \sqrt{2)}(2 \sqrt{2}+x)-4x }$

Answer 1

3-2√3 +x²-√36 +3√3 < 11 +x²- 8-4x

3+√3 +x² -6  < 3 +x² -4x

-3 +√3 < 3-4x 

-4x +3 > -3 +√3

-4x > -3+√3-3

-4x > -6+√3 |-1

4x < 6-√3

x < (6-√3)/4

x < (6-1,71)/4

x < 4,29/4

x < 1,0725  ⇒x∈{0;1}