A challenging math problem from Russia’s Unified State Exam (EGE) has sparked debate about the exam’s difficulty. The problem, designed for schoolchildren, involves finding the values of parameter ‘a’ for which a given equation has exactly two distinct roots.

The equation in question is at² – 2t – 49a + 18 = 0, derived from the original equation after a substitution of x – 9/x = t. The solution requires recognizing that x cannot be zero and then analyzing the discriminant of the quadratic equation.

The problem’s solution involves two main cases: when ‘a’ equals zero and when ‘a’ does not equal zero. When a = 0, the equation simplifies to a linear form (-2t + 18 = 0), yielding one solution. When ‘a’ is not zero, the quadratic equation must have a discriminant (D) equal to zero for it to have only one solution.

Calculating the discriminant leads to the equation 49a² – 18a + 1 = 0. Solving this quadratic equation provides the values of ‘a’ that satisfy the condition. The original equation has two solutions for these specific values of ‘a’, as well as when a = 0.

Reactions to the problem’s difficulty have been varied, with some expressing disbelief that it is intended for schoolchildren. Some people confessed they didn’t even try to solve it. Others admitted to needing significant time to find the solution. Some claimed to solve it quickly, while some confessed to guessing the answer.