Answer :
ANSWER:
5 positive integers
STEP-BY-STEP EXPLANATION:
We have the following inequality:
[tex]100\le x^2\le200[/tex]Solving for x:
[tex]\begin{gathered} \sqrt[]{100}\le\sqrt[]{x^2}\le\sqrt[]{200} \\ \pm10\le x\le\pm10\sqrt[]{2} \end{gathered}[/tex]Being only positive numbers, it would then remain:
[tex]10\le x\le10\sqrt[]{2}[/tex]Being only integers, it would then remain:
[tex]\begin{gathered} 10\le x\le10\sqrt[]{2} \\ 10\sqrt[]{2}=14.14\cong14 \\ \text{therefore:} \\ 10\le x\le14 \\ x=10,11,12,13,14 \end{gathered}[/tex]Which means that 5 positive integers satisfy the inequality (10, 11, 12, 13, 14)