Question 137
1) Prove that there is a triangle with side lengths
$$
\sqrt{a^{2}-a+1},\ \sqrt{a^{2}+a+1},\ \text{ and }\ \sqrt{4 a^{2}+3}.
$$
2) Prove that the area of this triangle does not depend on $a$.
$$
\sqrt{a^{2}-a+1},\ \sqrt{a^{2}+a+1},\ \text{ and }\ \sqrt{4 a^{2}+3}.
$$
2) Prove that the area of this triangle does not depend on $a$.