Question

помогите решить пожалуйста! 193,194,195 нечетные

Answer 1

1.
6y⁴-5y²-6=0
z=y²
6z²-5z-6=0
D=5²-4*(-6)*6=25+144=169=13²
$z_{1}= frac{-(-5)- sqrt{169} }{2*6} = frac{5-13}{12} = -frac{8}{12}=- frac{2}{3} \ z_{2}= frac{-(-5)+sqrt{169} }{2*6} = frac{5+13}{12} = frac{18}{12}=1.5$
y=√z
$y_{1}= sqrt{ frac{2}{3} } \ y_{2}= sqrt{ 1.5 }$

4.5m⁴-9m²+4=0
m²=t
4.5t²-9t+4=0
D=9²-4*4*4.5=81-72=9=3²
$t_{1}= frac{9- sqrt{9} }{2*4.5} = frac{9-3}{9} = frac{6}{9} = frac{2}{3} \ t_{2}= frac{9+sqrt{9} }{2*4.5} = frac{9+3}{9} = frac{12}{9} = frac{4}{3} \ m= sqrt{t} \ m_{1}= sqrt{ frac{2}{3} } \ m_{2}= sqrt{ frac{4}{3} }= frac{2}{ sqrt{3} }$

2.
$frac{1}{8} y^{4}- frac{7}{8} y^{2}-1=0 \ y^{2}=e \ frac{1}{8} e^{2}- frac{7}{8} e-1=0 \ D=( frac{7}{8})^{2}-4*(-1)* frac{1}{8} = frac{49}{64} + frac{4}{8} =frac{49}{64} + frac{32}{64} = frac{81}{64} = frac{9^{2}}{8^{2}} \ e_{1}= frac{ frac{7}{8}- frac{9}{8} }{2* frac{1}{8} } = -frac{2}{8} : frac{2}{8} =-frac{2}{8}* frac{8}{2} =-1 \ e_{2}= frac{ frac{7}{8}+ frac{9}{8} }{2* frac{1}{8} } =frac{16}{8} : frac{2}{8} =2* frac{8}{2} =8 \ y= sqrt{e}$
$y =sqrt{8}=2 sqrt{2}$

$frac{1}{144} n^{4}- frac{25}{144} n^{2}+1=0 \ n^{2}=p \ frac{1}{144} p^{2}- frac{25}{144} p+1=0 \ D=(frac{25}{144})^{2}-4*1*frac{1}{144}= frac{625}{20736} - frac{4}{144}= frac{625}{20736} - frac{1}{36} = frac{625}{20736} - frac{576}{20736}= \ =frac{49}{20736}= frac{7^{2} }{144^{2}} \ p_{1}= frac{ frac{25}{144} - frac{7}{144} }{2* frac{1}{144} } = frac{ frac{18}{144} }{ frac{2}{144} } = frac{18}{144} * frac{144}{2} =9$
$p_{2}= frac{ frac{25}{144} + frac{7}{144} }{2* frac{1}{144} } = frac{ frac{32}{144} }{ frac{2}{144} } = frac{32}{144} * frac{144}{2} =16\ \ n= sqrt{p} \ n_{1}= sqrt{9} =3 \ n_{2}= sqrt{16} =4$



3.
(2x-7)²-11(2x-7)+30=0
4x²-28x+49-22x+77+30=0
4x²-50x+156=0
D=2500-4*4*156=2500-2496=4=2²
$x_{1}= frac{50-2}{2*4} =- frac{48}{8} =-6 \ x_{1}= frac{50+2}{2*4} =- frac{52}{8} =6.5$

(6x+1)²+2(6x+1)-24=0
36x²+12x+1+12x+2-24=0
36x²+24x-21=0
D=24²-4*(-21)*36=576+3024=3600=60
$x_{1}= frac{-24-60}{2*36} = -frac{84}{72} =- frac{7}{6} \ x_{2}= frac{-24+60}{2*36} = frac{36}{72} = 0.5$