Use the Rational Zero Theorem to list all possible rational zeros for the given function. \( f(x)=11 x^{3}-x^{2}+3 \)

If the two middle terms in the expansion of \( (a x+b)^{2 n+1} \) are equal, then find \( x \) \( a=2 b \)

Rationalize the denominator of \( \frac{7}{2 + \sqrt{3}} \).

14. \( (2 a-7 b)(2 a+7 b)_{\mathrm{Ypx}} \)

Soient xety deux nombres reels tels que \( : x \leq \frac{1}{2}, y \geq \frac{3}{2} \) et \( x-2 y=5 \) On pose \( A=\sqrt{x^{2}+(x-1)^{2}+2 x(x-1)} \) et \( B=\sqrt{4 y^{2}+(2 y-3)^{2}+4 y(2 y-3)} \) 1) Montrer que : \( A=\sqrt{(2 x-1)^{2}} \) et \( B=\sqrt{\left(4 y-3 t^{2}\right.} \) 4) Simplifier Ies nombres \( A \) et \( B \) 8) Determiner la valeur numérique du nombre \( A+3 \) X

a) \( \left(\frac{25}{3}\right)^{\frac{1}{2}}-\left(\frac{1}{3}\right)^{-\frac{1}{2}} \)