- #1

chwala

Gold Member

- 2,697

- 360

- Homework Statement
- See attached

- Relevant Equations
- Inequalities

Find solution here;

Ok i just want clarity for part (a),

My approach is as follows, since we want positive integer values that satisfy the problem then,

##\dfrac {n^2-1}{2}≥1## I had earlier thought of ##\dfrac {n^2-1}{2}≥0## but realized that ##0## is an integer yes but its not a positive integer.

Therefore,

##\dfrac {n^2-1}{2}≥1, n^2-1≥2, n^2≥3 ⇒n≥\sqrt 3##

For,

##\dfrac {n^2+1}{2}≥, n^2≥1⇒n≥1##. The inequality satisfying the two is

##n≥\sqrt 3##

...Any insight on this is appreciated.

Part (b) is easy...no problem there...