Mam zadanie z matematyki rozwiąż równanie 16-(3x-1)do kwadratu=0 9xkwadrat-(2x-1)do kwadratu=0(2x+1.... Question from @sebastian23071996

krysta $a)\\ \\16-(3x-1)^2=0\\ \\16-(9x^2-6x+1)=0\\ \\16-9x^2+6x-1=0\\ \\-9x^2+6x+15=0\\ \\\Delta =b^2 -4ac =6^{2}-4*(-9)*15=36+540=576\\ \\\sqrt{\Delta }=\sqrt{576}=24$

$x_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{-6-24}{2*(-9)}=\frac{-30}{-18}=\frac{5}{3}=1\frac{2}{3}\\ \\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}=\frac{-6+24}{2*(-9)}=\frac{18}{-18}= -1$

$b)\\ \\9x^2-(2x-1)^2=0\\ \\9x^2-(4x^2-4x+1)=0\\ \\9x^2-4x^2+4x-1=0\\ \\5x^2+4x-1=0\\ \\\Delta =b^2 -4ac =4^{2}-4*5*(-1)=16+20=36\\ \\\sqrt{\Delta }=\sqrt{36}=6$

$x_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{-4-6}{2*5}=\frac{-10}{10}=-1\\ \\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}=\frac{-4+6}{2*5}=\frac{2}{10}=\frac{1}{5}$

$c)\\ \\(2x+1)^2=(4x+5)^2\\ \\4x^2+4x+1=16x^2+40x+25\\ \\4x^2+4x+1-16x^2-40x-25=0\\\\-12x^2-36x-24=0/:(-12)\\ \\x^{2}+3x+2=0\\ \\\Delta =b^{2}-4ac =3^2-4*1*2=9-8=1$

$\sqrt{\Delta }=\sqrt{1}=1\\ \\x_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{-3-1}{2}=\frac{-4}{2}=-2\\ \\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}=\frac{-3+1}{2}=\frac{-2}{2}=-1$

2 votes Thanks 1

sebastian23071996 Dziękuje

krysta :)

Zgłoś nadużycie! 9xkw-(2x-1)kw=0
9xkw-(4xkw-4x+1)=0
9xkw-4xkw+4x-1=0
5xkw+4x-1=0
a=5 b =4 c= - 1
delta = bkw- 4ac
delta = 4kw -4 razy5 razy-1= 16+20=36
pierwiastek z delty = 6
x1 = - b - pirw z delty przez 2 a
x1= -4 -6/ 2razy 5=-10/10= -1

x2=-4+6/2 razy 5 = 2/10=1/5

16-(3x-1) do kw=0
16-(9xkw-6x+1)=0
16-9xkw+6x-1=0
-9xkw+6x+15=0/-3
3xkw-2x - 5=0
delta = -2 kw - 4 razy 3 razy -5= 4+60=64
pierwiastek z delty 8
x1= 2-8/2razy3=-6/6 = -1
x2 = 2+8/ 2razy3 = 10/6= 5/3

(2x+1) kw= (4x+5)kw
4xkw+4x+1=16xkw+8x+25
4xkw+4x +1 -16xkw - 8x-25 =0
-12xkw -4x -24 =0/ -4
3xkw +x + 6=0
delta = 1kw - 4razy3 razy6 = 1-72=-71 brak rozwiązania

1 votes Thanks 0

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