Difficult

Parametric Linear Equations: Very Difficult Problems with Solutions

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