B3
$\begin{array}{l}
{S_1} = {5^{15}} = {\rm{30517578125}}\\
{S_2} = \dfrac{1}{2}(f(1) - f( - 1)) = \dfrac{1}{2}({\rm{30517578125 +1) = 15258789063}}
\end{array}$
Tìm x,y $ \in $ N* sao cho
$\begin{array}{l}
{B_1}:\\
\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{1}{3} + \dfrac{1}{{xy}}
\end{array}$
$\begin{array}{l}
{B_2}:\\
D = 1 + \dfrac{1}{3} + \dfrac{1}{5} + .... + \dfrac{1}{{2n + 1}}(n \in N)
\end{array}$
Tìm n nhỏ nhất D>4
$\begin{array}{l}
{B_3} = {(2 + x + 2{x^3})^{15}} = {a_0} + {a_1}x + {a_2}{x^2} + ...... + {a_{45}}{x^{45}}\\
{S_1} = {a_1} + {a_2} + {a_3} + ...... + {a_{45}}\\
{S_2} = {a_0} + {a_2} + {a_4} + ..... + {a_{44}}
\end{array}$
B3
$\begin{array}{l}
{S_1} = {5^{15}} = {\rm{30517578125}}\\
{S_2} = \dfrac{1}{2}(f(1) - f( - 1)) = \dfrac{1}{2}({\rm{30517578125 +1) = 15258789063}}
\end{array}$
B3:${S_1} = {S_2} = 30517545357$ đúng hok tak
B1:
CMTT ta dc
Rùi xài table ra các cặp
B1:$\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{1}{3} + \dfrac{1}{{xy}}(x,y \in {N^*}) \leftrightarrow \dfrac{{x + y}}{{xy}} = \dfrac{{xy + 3}}{{3xy}}$
$\begin{array}{l}
\leftrightarrow 3{x^2}y + 3x{y^2} = {x^2}{y^2} + 3xy \leftrightarrow 3{x^2}y + 3x{y^2} - {x^2}{y^2} - 3xy = 0\\
\leftrightarrow xy\left( {3x + 3y - xy - 3} \right) = 0 \leftrightarrow 3x + 3y - xy - 3 = 0\\
\leftrightarrow y(3 - x) = 3 - 3x \leftrightarrow y = \dfrac{{3 - 3x}}{{3 - x}} \leftrightarrow \left[ \begin{array}{l}
\left\{ \begin{array}{l}
3 - 3x > 0\\
3 - x > 0
\end{array} \right.\\
\left\{ \begin{array}{l}
3 - 3x < 0\\
3 - x < 0
\end{array} \right.
\end{array} \right. \leftrightarrow \left[ \begin{array}{l}
x < \dfrac{1}{3}\\
x > 3
\end{array} \right. \leftrightarrow x > 3
\end{array}$
CMTT ta dc $y > 3$
Rùi xài table ra các cặp
$(x;y) = (4;9),(5;6),(6;5),(9;4)$ Mệt