1)
5х² +9х - 4 = 0
а= 5 ; b = 9 ; с = -4
2)
а) 2х² + 50х = 0
2х(х + 25) = 0
2х = 0
х₁ = 0
х + 25 = 0
х₂ = - 25
б)х² - 9 = 0
х² = 9
х₁ = √9
х₁ = 3
х₂ = - √9
х₂ = - 3
в)2х² + 7х - 9 = 0
а=2 ; b = 7; с = -9
D = 7² - 4*2*(-9)= 49 + 72 = 121 =11²
D>0 - два корня уравнения
х₁ = ( - 7 - 11)/(2*2) = - 18/4 = -4,5
х₂ = (-7 + 11)/(2*2) = 4/4 = 1
г)х² -16х + 63 =0
а= 1 ; b = - 16; с = 63
D = (-16)² - 4*1*63 = 256 -252 = 4 = 2² ; D>0
x₁ = ( - (-16) - 2)/(2*1) = (16-2)/2 = 14/2 = 7
x₂ = ( - (-16) + 2)/(2*1)= (16+2)/2 = 18/2 = 9
3)
a) (10x+3)/6 = 3/x
х(10х + 3) = 6*3
10х² + 3х = 18
10х² + 3х - 18 = 0
а= 10 ; b = 3 ; с = - 18
D = 3² -4*10*(-18) = 9 +720= 729 = 27² ; D>0
x₁ = (- 3 - 27)/(2*10) = - 30/20 = - 3/2 = - 1.5
x₂ = ( - 3 + 27)/(2*10) = 24/20 = 12/10 = 1,2
б) (х + 4)² = (3х - 2)(х - 8)
х² + 2*х*4 + 4² = 3х² - 24х - 2х + 16
х² + 8х + 16 = 3х² - 26х + 16
3х² - 26х + 16 - х² -8х - 16 = 0
2х² - 34х = 0
2х(х - 17) = 0
2х = 0
х₁ = 0
х - 17 = 0
х₂ = 17