8.1. The monthly pension of football fan Ivan Ivanovich is

$$
\frac{149^{6}-199^{3}}{149^{4}+199^{2}+199 \cdot 149^{2}}
$$

rubles, and the cost of a ticket to a World Cup match is 22000 rubles. Will Ivan Ivanovich's pension for one month be enough to buy one ticket? Justify your answer.
Solution: Let $149^{2}=a, 199=b$. Then Ivan Ivanovich's monthly pension (in rubles) is

$$
\frac{a^{3}-b^{3}}{a^{2}+b^{2}+a \cdot b}=\frac{(a-b)\left(a^{2}+a b+b^{2}\right)}{a^{2}+a b+b^{2}}=a-b=149^{2}-199=22002
$$

Thus, his pension will be enough for one ticket.

Answer: It will be enough.

Recommendations for checking:

| is in the work | points |
| :--- | :--- |
| Correct and fully justified answer | 7 points |
| Arithmetic errors were made in the calculations, possibly leading to an incorrect answer | deduct 2 points for each |
| The formula for the difference of cubes was applied and the fraction was simplified | 5 points |
| The problem was reduced to algebra by introducing variables (one or two), but not solved | 3 points |
| Answer without justification and/or incorrect answer | 0 points |