SUBIECTUL 2

a) If $x$ is a real number and $x(x+1)=12$, calculate the value of the expression $E(x)=x^{4}+2 x^{3}+2 x^{2}+x$.

b) Show that $A=\sqrt{a^{4}+2 a^{3}+2 a^{2}+a}$ is irrational for any non-zero natural number $a$.

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