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\begin{document}
\begin{enumerate}

\item {\large\bf '99�Z���^�[�{���� \ ���wI �E ���wA \ �K�����(�z�_40)}\\
$�m1�na,b�����R���Ƃ�,2���֐� \\
 y=x^2 -4ax+4a^2-4a-3b+9 \\
�̃O���t��C�Ƃ���.���̎�,C�̒��_�̍��W�� \\
([�A]a,-[�C]a-[�E]b+[�G]) \\
�̕������ł���.$ \\

\begin{enumerate}

\item $�O���tC��x���ƌ����Ȃ��Ƃ�\\
a=�m�I�n,b=[�J] \\ 
�ł���.$
\vfill

\item $2�������� \\
x^2-4ax+4a^2-4a-3b+9=0 \\
����̉������Ƃ���.���̓�̉��̍��� 2\sqrt{11} �ł���Ƃ�\\
4a+3b=[�L�N] \\
�ł���.����������,a,b�̒l�� \\
a=[�P],b=[�R] �ł���.$
\vfill

\item $ �O���tC��y��������-3�������s�ړ���,�����x���Ɋւ��đΏ� \\
�ړ������2���֐�y=-x^2+8x+1 �̃O���t�ɂȂ�Ƃ���. \\
���̂Ƃ� \\
a=[�T],b=[�V] \\
�ł���.$
\vfill
\end{enumerate}


[2]�@$�Ԑ��΂�4�F�̃J�[�h��5�����v20������.�e�F�̃J�[�h�� \\
��,���ꂼ��1����5�܂ł̔ԍ�����������Ă���.����20���̒��� \\
��3������x�Ɏ��o��.$ \\

\begin{enumerate}
\item $3�������ׂē����ԍ��ƂȂ�m����
\frac{[�X]}{[�Z�\]}  �ł���.$
  \vfill
\item $3�����F���ԍ��������ׂĈقȂ�m����
\frac{[�^]}{[�`�c]}  �ł���.$
  \vfill
\item $3���̂����ɐԂ��J�[�h�����傤��1���܂܂��m����
\frac{[�e�g]}{[�i�j]}  �ł� \\
��.$
\vfill
\item $3���̒��ɂ���Ԃ��J�[�h�̖����̊��Ғl�� \frac{[�k]}{[�l]}  �ł���.$
\vfill
\end{enumerate}


% ==========================================================================

\item {\large\bf '99�Z���^�[�{���� \ ���wI�E���wA \ �K�����(�z�_40)}

\begin{enumerate}
\item $a,b,c,d ��萔�Ƃ���.x�ɂ��Ă�2�̐��� \\
A=x^2+x-1,B=x^4+ax^3+bx^2+x+2 \\
�ɑ΂���,B��A�Ŋ������Ƃ�,����A+c��,�]�肪d�ƂȂ�Ƃ� \\
��.���̂Ƃ� \\
a=[�A],b=[�C],c=[�E],d=[�G] \\
�ł���.�܂� \\
x=\frac{-1+\sqrt{17}}{2} \\
�̂Ƃ� \\
A=[�I],B=[�J�L] \\
�ł���.$
\vfill 
\vfill 
\vfill 
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\newpage 

\item  $ ����a,b�ɂ��Ď��̏������l����.  \\
\MARU{0} \ \ a>0 ���� b>0 \\
\MARU{1} \ \ a+b>0  \\
\MARU{2} \ \ |a|+|b|>0  \\
\MARU{3} \ \ a+b>0 ���� ab>0  \\
\MARU{4} \ \ 2���֐�y=x^2-ax+b �̃O���t��,x���̐��̕�����2�_ \\
�Ō���� \\
\MARU{1} \sim \MARU{4} ������,\MARU{0} �Ɠ��l�ȏ����́m�P�n�ł���. \ �܂� \MARU{1} \sim \MARU{4} �� \\
������, [�P]�͑��̂��ׂĂ̏����̏\�������ł���,[�R] �͑��̂� \\
�ׂĂ̏����̕K�v�����ł���. \\
�@�����\MARU{0}�̔ے�Ɠ��l�ȏ����͎���\MARU{5}���� \MARU{8} �̂���[�T]�ł���.$\\
$\MARU{5} \ \ a+b \leq  0  ���� ab\leq 0 \\
\MARU{6} \ \ a+b \leq  0  �܂��� ab\leq 0 \\
\MARU{7} \ \ a<0  �܂��� b<0  \\
\MARU{8} \ \ a<0   ����  b<0 $ \\
\vfill 

\item $�~�ɓ��ڂ���l�p�`ABCD �� \\
AB=BC=2 \sqrt{2} ,BD=2 \sqrt{3}, \angle ABC=120^{\circ} \\
�𖞂����Ƃ���.������,AD>CD�Ƃ���.���̂Ƃ� \\
AC=[�V]\sqrt{[�X]} , \angle BDC =[�Z�\]^{\circ}  \\
 �ł���.\\
�܂�
AD=[�^]+\sqrt{[�`]} ,CD =[�^]-\sqrt{[�`]} \\
�ł���,�l�p�`ABCD �̖ʐς� [�c]\sqrt{[�e]}  �ł���.$

\end{enumerate}

% ====================================================================

\item {\large\bf '99�Z���^�[�{���� \ ���wI�E���wA \ �I����(�z�_20)}\\

$������-100�Ō�����5�̓������� \{ a_n \} �̈�ʍ��� \\
a_n=[�A](n-[�C�E]) \\
�ł���.���̐�������̂悤��1��,2��,2^2��,2^3�� \cdots �Ƌ��ɕ�����.\\
|a_1|a_2 \ a_3 |a_4 \ a_5 \ a_6 \ a_7 | a_8 \  \cdots $ \\

\begin{enumerate}
\item $m�Ԗڂ̋��̍ŏ��̍���b_m�Ƃ����� \\ 
b_8=[�G�I�J] \\
�ł��� \\
b_1+b_2+b_3+ \cdots +b_8 =[�L�N�P] \\
�ł���. \\ $
\vfill

\item $ 6�Ԗڂ̋��ɓ��鍀�̘a�� [�R�T�V�X] �ł���. $
\vfill
\end{enumerate}


% ==========================================================================

\item {\large\bf '99�Z���^�[�{���� \ ���wI�E���wA \ �I����(�z�_20)} \\

$\triangle ABC �̕�AB,AC��ɂ��ꂼ��_D,E�� \\
\ \ \ AD:DB=t:1,  AE:EC=1:(t+1)  \\
�ƂȂ�悤�ɂƂ�.\\
\ \ �����,BE��CD�̌�_��A�����Ԓ�����BC�ƌ����_��F�Ƃ���.\\
\ \ ���̕�����[�G�I] \sim [�V�X]�ɂ��Ă�,���Ă͂܂镶����A \sim F �̂��� \\
����I��.������,�G�ƃI,�J�ƃL,�N�ƃP,�R�ƃT,�V�ƃX�͂��ꂼ��� \\
�̏�������Ȃ�. $ \\



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\newpage
\begin{enumerate}  
\item $ DE��BC�ɕ��s�ɂȂ�Ƃ� \\
t=\frac{[�A�C]+\sqrt{[�E]}}{2} \\
�ł���.$ 
\vfill 
\item $ \triangle ABF �� \triangle AFC �̖ʐς����ꂼ��S_1,S_2 �Ƃ���Ƃ� \\
S_1:S_2=[�G�I]:[�J�L]\\
=[�N�P] \sin \angle BAF : [�R�T] \sin \angle FAC \\
�ł���.�܂�,AF�� \triangle ABC�̓��S��ʂ�Ȃ�� \\
BF:FC=[�V�X]:AC \\
�ł���,�����AC=12AB �̂Ƃ�   \\
t=[�Z] \ \ �ł���.$
\vfill \vfill 
\end{enumerate}

% ============================================================================

\item {\large\bf '99�Z���^�[�{���� \ ���wI�E���wA \ �I����(�z�_20)}\\

\ \ $���̗���}��,0�ȏ�̐����������̏��ɓ��͂���,�Ō�ɕ��̐���� \\
�͂�,���͂��ꂽ���̂����ő�̂��̂��o�͂�����@�����������̂ł���.�ϐ� \\
A�����͂��ꂽ����\��,�ϐ�B������܂łɓ��͂��ꂽ���̂Ȃ��ł����Ƃ��傫 \\
������\���Ƃ���.$
 \\

\begin{enumerate}
\item $ [�A] \sim [�I]�ɓK������̂�,���� \MARU{0} \sim \MARU{7} �̂�������I��
\\
\MARU{0}\ \ A����͂��� \\
\MARU{1}\ \ B���o�͂��� \\
\MARU{2}\ \ A��B�������� \\
\MARU{3}\ \ B��A�������� \\
\MARU{4}\ \ A�͕��� \\
\MARU{5}\ \ B�͕��� \\
\MARU{6}\ \ A��B���傫���� \\
\MARU{7}\ \ B��A���傫���� \\ $

\item $15,13,16,16,20,1,99,-1 �Ɠ��͂��ꂽ�Ƃ� $\\
\end{enumerate}

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