Rozwiązane

d) 28 x do 2 - 4x + w ułamku 1/7 = 0 e) -x do 2 - 2x - 1 = 0 f) w ułamku 1/2 x do 2 - 2x -1=0



Odpowiedź :

Cyna4

Zadanie 1

[tex]28x^2-4x+\dfrac{1}{7}=0\\\\196x^2-28x+1=0\\\\a=196,\ b=-28,\ c=1\\\\\Delta=b^2-4ac=(-28)^2-4\cdot196\cdot1=784-784=0\\\\x_0=\dfrac{-b}{2a}=\dfrac{28}{392}=\dfrac{1}{14}\\\\\boxed{x\in\Big\{\dfrac{1}{14}\Big\}}[/tex]

Zadanie 2

[tex]-x^2-2x-1=0\\\\x^2+2x+1=0\\\\(x+1)^2=0\\\\x+1=0\\\\\boxed{x=-1}[/tex]

Albo:

[tex]a=1,\ b=2,\ c=1\\\\\Delta=b^2-4ac=2^2-4\cdot1\cdot1=4-4=0\\\\x_0=\dfrac{-b}{2a}=\dfrac{-2}{2}=-1\\\\\boxed{x\in\{-1\}}[/tex]

Zadanie 3

[tex]\dfrac{1}{2}x^2-2x-1=0\\\\x^2-4x-2=0\\\\a=1,\ b=-4,\ c=-2\\\\\Delta=b^2-4ac=(-4)^2-4\cdot1\cdot(-2)=16+8=24\\\\\sqrt{\Delta}=2\sqrt{6}\\\\x_1=\dfrac{-b-\sqrt{\Delta}}{2a}=\dfrac{4-2\sqrt{6}}{2}=2-\sqrt{6}\\\\x_2=\dfrac{-b+\sqrt{\Delta}}{2a}=\dfrac{4+2\sqrt{6}}{2}=2+\sqrt{6}\\\\\boxed{x\in\{2-\sqrt{6},2+\sqrt{6}\}}[/tex]