normal

# Problems using Vieta's formulas - normal

Problem №1
If $x_1, x_2$ are the roots of the equation $x^2+5x-3=0$, determine the value of $x_1^2+x_2^2$.
Problem №2
If $x_1, x_2$ are the roots of the equation $x^2+11x+12=0$, determine the value of $x_1^2+x_2^2$.
Problem №3
If $x_1, x_2$ are the roots of the equation $x^2+9x+33=0$, determine the value of $\frac{1}{x_1}+\frac{1}{x_2}$.
Problem №4
If $x_1, x_2$ are the roots of the equation $x^2-8x+11=0$, determine the value of $x_1^3+x_1^2+x_1+x_2^3+x_2^2+x_2$.
Problem №5
If $x_1, x_2$ are the roots of the equation $x^2-15x+36=0$, determine the value of $|x_1-x_2|$.
Problem №6
Let $x_1, x_2$ be the roots of the equation $x_^2-12x+19=0$. Determine the value of $x_1(1-x_1)+x_2(1-x_2)$.
Problem №7
If $x_1, x_2$ are the roots of the equation $x^2-4x+1=0$, determine the value of $(x_1-\frac{1}{x_1})^2+(x_2-\frac{1}{x_2})^2$.
Problem №8
If $x_1, x_2$ are the solutions to the equation $x^2-5x+a^2-2a+1=0$ where $a \in R$. Find the value of a, for which $x_1x_2$ is minimal.

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