Algebra Selected AMC 10 Practice Problems

[2020 AMC 10B] What is the sum of all real numbers \(x\) for which \(|x^2-12x+34|=2?\)

\(\textbf{(A) } 12 \qquad \textbf{(B) } 15 \qquad \textbf{(C) } 18 \qquad \textbf{(D) } 21 \qquad \textbf{(E) } 25\)

[2006 AMC 10B]

Let a and b be the roots of the equation \(x^2-mx+2=0\). Suppose that \(a+\frac1b\) and \(b+\frac1a\) are the roots of the equation \(x^2-px+q=0\). What is \(q\)?

\(\mathrm{(A) \ } \frac{5}{2}\qquad \mathrm{(B) \ } \frac{7}{2}\qquad \mathrm{(C) \ } 4\qquad \mathrm{(D) \ } \frac{9}{2}\qquad \mathrm{(E) \ } 8\)

[2013 AMC 12A] Given that  and  are distinct nonzero real numbers such that , what is ?

Suppose that real number x satisfies $$\sqrt{49-x^2}-\sqrt{25-x^2}=3$$ What is the value of \(\sqrt{49-x^2}+\sqrt{25-x^2}\)?

\(\textbf{(A) }8\qquad \textbf{(B) }\sqrt{33}+8\qquad \textbf{(C) }9\qquad \textbf{(D) }2\sqrt{10}+4\qquad \textbf{(E) }12\qquad\)