2,85 rozwiaz rowniania(3x-1)(4x+5)=(4x+5)(2x-1)3x²+25=081-(x-2)²=0-4x²+44x-121=0-x²-√2x=025(x-1)²-9(.... Question from @toemk

toemk @toemk

November 2018 1 25 Report

2,85 rozwiaz rowniania

(3x-1)(4x+5)=(4x+5)(2x-1)

3x²+25=0

81-(x-2)²=0

-4x²+44x-121=0

-x²-√2x=0

25(x-1)²-9(x+2)²=0

2,99

rozwiaz nierownosci

x²+5x+8>0

2x²-x+7<0

(x-3)(2x-5)<4x²-2x-20

4x²-1<(2x-1)(x+3)

krysta

2,85

$(3x-1)(4x+5)=(4x+5)(2x-1)\\12x^2+15x-4x-5 = 8x^2-4x+10x-5\\12x^2+15x+4x- 8x^2-4x-10x=-5+5\\4x^{2}-5x=0\\x(4x-5)=0\\x=0\vee 4x-5=0\\x=0\vee 4x=5\mid \div 4\\x=0\vee x=\frac{3}{5}$

3x²+25=0

równanie sprzeczne , kwadrat danej liczby , zawsze jest liczba dodatnią

$81-(x-2)^{2}=0\\81-(x^{2}-4x+4)=0\\81-x^{2}+4x-4=0\\-x^{2}+4x+77=0\\\Delta =b^2-4ac =4^2-4\cdot (-1)\cdot 77=16+308= 324\\\sqrt{\Delta }=\sqrt{324}=18\\x_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{-4-18}{2\cdot (-1)}=\frac{-22}{-2}=11\\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}=\frac{-4+18}{2\cdot (-1)}=\frac{14}{-2}=-7$

$-4x²+44x-121=0\\\Delta =b^2-4ac =44^2-4\cdot (-4)\cdot (-121)=1936-1936=0\\x_{0}=\frac{-b }{2a}=\frac{-44}{2\cdot (-4)}=\frac{-44}{-8}=\frac{11}{2}=5\frac{1}{2}$

$-x^{2}-\sqrt{2}x=0\\-x(x+\sqrt{2})=0\\-x=0\vee x+\sqrt{2}=0\\x=0\vee x=-\sqrt{2}$

$25(x-1)^{2}-9(x+2)^{2}=0\\25(x^{2}-2x+1)-9(x^{2}+4x+4)=0\\25x^{2}-50x+25-9x^{2}-36x-36=0\\16x^{2}-86x-11=0\\\Delta =b^2-4ac =(-86)^2-4\cdot 25\cdot (-11)=7396+704=8100\\\sqrt{\Delta }=\sqrt{8100}=90\\x_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{86-90}{2\cdot 16}=\frac{-4}{32}=-\frac{1}{8}\\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}=\frac{86+90}{2\cdot 16}=\frac{176}{32}=\frac{11}{2}=5\frac{1}{2}$

zad. 2,99

$x^{2}+5x+8>0\\\Delta =b^2-4ac =5^2-4\cdot 1\cdot 8=25-32=-8$

a>0 i ∆ < 0

$x\epsilon R$

$2x²-x+7<0\\\Delta =b^2-4ac =(-1)^2-4\cdot 2\cdot 2=1-16=-15$

a>0 , ∆ < 0 zbór pusty

$(x-3)(2x-5)< 4x^{2}-2x-20\\2x^{2}-5x-6x+15< 4x^{2}-2x-20\\2x^{2}-5x-6x+15-4x^{2}+2x+20< 0\\-2x^{2}-9x+35< 0\\\Delta =b^2-4ac =(-9)^2-4\cdot (-2)\cdot 35=81+280=361\\\sqrt{\Delta }=\sqrt{361}=19\\x_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{9-19}{2\cdot (-2)}=\frac{-10}{-4}=\frac{5}{2}=2\frac{1}{2}\\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}=\frac{9+19}{2\cdot (-2)}=\frac{28}{-4}=-7$

a< 0 , ramiona paraboli są skierowane w dół

$x\epsilon (-7,2\frac{1}{2})$

$4x^{2}-1< (2x-1)(x+3)\\4x^{2}-1< 2x^{2}+6x-x-3\\4x^{2}-1- 2x^{2}-6x+x+3< 0\\2x^{2}-5x+2< 0\\\Delta =b^2-4ac =(-5)^2-4\cdot 2\cdot 2=25-16=9\\\sqrt{\Delta }=\sqrt{9}=3\\x_{1}=\frac{-b-\sqrt{\Delta }}{2a}=\frac{5-3}{2\cdot 2}=\frac{2}{4}=\frac{1}{2}\\x_{2}=\frac{-b+\sqrt{\Delta }}{2a}=\frac{5+3}{2\cdot 2}=\frac{8}{4}=2$