Question 153
Assume that real numbers $a$ and $b$ satisfy
$$
a b + \sqrt{a b + 1} + \sqrt{a^{2} + b} \cdot \sqrt{b^{2} + a} = 0
$$
Find, with proof, the value of
$$
a \sqrt{b^{2} + a} + b \sqrt{a^{2} + b}
$$
$$
a b + \sqrt{a b + 1} + \sqrt{a^{2} + b} \cdot \sqrt{b^{2} + a} = 0
$$
Find, with proof, the value of
$$
a \sqrt{b^{2} + a} + b \sqrt{a^{2} + b}
$$