Aku n MATEMATIKA cah SMA Nda: Jawaban speed problem Math 01

NO.1

$\dpi{100} \fn_cs x_{1}+x_{2}=6\, \, dan\, \, x_{1}.x_{2}=2$

$\dpi{100} \fn_cs x^{3}_{1}.x_{2}+x_{1}.x^{3}_{2}=(x_{1}.x_{2}).({\color{Red} x^{2}_{1}+x^{2}_{2}})=(x_{1}.x_{2}).({\color{Red} (x_{1}+x_{2})^{2}-2.x_{1}.x_{2}} )$

$\dpi{100} \fn_cs (2).((6)^{2}-2.2)=2.(32)=64.......(B)$

NO. 02

$\dpi{100} \fn_cs f''(x)=6x+10$

$\dpi{100} \fn_cs f'(x)=\int (6x+10).dx=3x^{2}+10x+c$
$\dpi{100} \fn_cs f(x)=\int (3x^{2}+10x+c).dx=x^{3}+5x^{2}+cx+d$
$\dpi{100} \fn_cs f(1)=1^{3}+5.1^{2}+c.1+d=4\Rightarrow c+d=-2.......(i)$
$\dpi{100} \fn_cs f(2)=2^{3}+5.2^{2}+c.2+d=18\Rightarrow 2c+d=-10.......(ii)$
dari persamaan (i) dan (ii) dengan Eliminasi or Substitusi
or Invers matrik or cara Determinan
didapat kan c = - 8 dan d = 6 sehingga

$\dpi{100} \fn_cs f(x)=x^{3}+5x^{2}-8x+6\Rightarrow f(-1)=(-1)^{3}+5(-1)^{2}-8.(-1)+6 = 18....(D)$

NO. 03

$\dpi{100} \fn_cs \left (\frac{2x-1}{x+5} -3 \right ).\left (\frac{2x-1}{x+5}+3 \right )\leqslant 0$
$\dpi{100} \fn_cs \left (\frac{2x-1}{x+5} -3.\left ( {\color{Blue} \frac{x+5}{x+5}} \right ) \right ).\left (\frac{2x-1}{x+5}+3.\left ( {\color{Blue} \frac{x+5}{x+5}} \right ) \right )\leqslant 0$
$\dpi{100} \fn_cs \frac{(-x-16).(5x+14)}{(x+5)^{2}}\leqslant 0$