Difficult

# Parametric Linear Equations: Very Difficult Problems with Solutions

Problem 1
Let A be the set of numbers a, for which the equation $$(a+10)(a+8)(a+6)(a+4)(a+2)a(a-2)(a-4)(a-6)(a-8)(a-10)x=a+10$$ has no solutions for x. Determine the product of all elements of A.
Problem 2
Let $$A (a_1,a_2,\dots ,a_n)$$ be the set of natural numbers a, which satisfy the condition $$3<2a<15$$. Let $$x_1,x_2,\dots,x_n$$ be the solutions to the equation $$(a^2-1)x=a^2+2a+1$$. Find the product $$x_1 x_2 \dots x_n$$
Problem 3
Find the value of a, for which the equation
$$(a^2-7a+10)x=a^2-8a+15$$ has all $$x \in R$$ as solutions.
Difficult

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