6)
x² +14x + 45 = 0
D = 14² - 4*1*45 = 196 - 180 = 16 = 4²
D>0 - два корня уравнения
x₁ = (-14 - 4)/(2*1) = -18/2 = - 9
x₂ = (-14 +4)/(2*1) = -10/2 = - 5
7)
х²+3х - 70 = 0
D = 3² - 4*1*(-70) = 9 + 280 = 289 =17²
D>0 - два корня уравнения
х₁ = (- 3 - 17)/(2*1) = -20/2 = - 10
х₂ = (- 3 +17)/(2*1) = 14/2 = 7
8)
х²-12х +35 =0
D= (-12)² - 4*1*35 = 144 -140= 4 = 2²
D>0
x₁ = (- (-12) -2)/(2*1) = (12-2)/2 = 10/2=5
x₂ = (12+2)/2 = 14/2 =7
9)
x² - 9x + 20 = 0
D = (-9)² - 4*1*20 = 81 - 80 = 1 = 1²
D>0
x₁ = ( - (-9) - 1)/(2*1) = (9-1)/2 = 8/2 = 4
x₂ = (9 +1)/2 = 10/2 = 5
10)
x² - 20x - 69 = 0
D = (-20)² - 4*1*(-69) = 400+ 276 = 676=26²
D>0
x₁ = (- (-20) - 26)/(2*1) = (20-26)/2 = -6/2 = -3
x₂ = (20 +26)/2 = 46/2 = 23
11)
(x - 2)² +2x = 7(x - 2)
x² - 2*x *2 + 2² + 2x = 7x - 14
x² - 4x + 4 + 2x = 7x - 14
x² - 2x + 4 -7x + 14 = 0
x² - 9x + 18 = 0
D = (-9)² - 4*1*18 = 81- 72 = 9 =3²
D>0
x₁ = ( - (-9) - 3)/(2*1) = (9 - 3)/2 = 6/2 = 3
x₂ = (9 + 3)/2 = 12/2 = 6
12)
(2x - 1) / (x - 1) = (7x - 1) /(2x+2)
x - 1≠0 ; х≠ 1
2х + 2≠ 0 ; х≠ - 1
(х - 1)(7х - 1) = (2х - 1)(2х + 2)
7х² - х -7х + 1 = 4х² +4х - 2х - 2
7х² - 8х + 1 = 4х² + 2х - 2
7х² - 8х + 1 - 4х² - 2х + 2 = 0
3х² - 10х + 3 = 0
D = ( -10)² - 4*3*3 = 100 - 36 = 64 = 8²
D>0
x₁ = ( - (-10) - 8) / (2*3) = (10 - 8)/6 = 2/6 = 1/3
x₂ = (10 +8)/6 = 18/6 = 3
13)
(x+8)/x = (x +2)/2
x≠ 0
x(x+2) = (x+8) * 2
x² +2x = 2x + 16
x² +2x - 2x - 16 = 0
x² - 16 = 0
x² - 4² = 0
(x -4)(x+4) = 0
произведение = 0, если один из множителей = 0
х - 4 = 0
х₁ = 4
х + 4 = 0
х₂ = - 4
14)
х⁴- 3х² - 4 =0
замена х² = t
t² - 3t - 4 =0
D = (-3)² - 4*1*(-4) = 9 + 16 = 25 = 5²
D>0
t₁ = ( - (-3) - 5)/(2*1) = (3 - 5)/2 = -2/2 = -1
t₂ = ( 3 +5)/2 = 8/2 = 4
x² = - 1 нет решений
х² = 4
х₁= √4
х₁ = 2
х₂ = - √4
х₂ = - 2
15)
3х/5 = (х²+8)/10 | *10
3x *2 = x² + 8
6x = x² + 8
x² + 8 - 6x = 0
x² - 6x +8 =0
D= (-6)² -4*1*8 = 36-32=4=2²
D>0
x₁ = ( - (-6) - 2)/(2*1) = (6-2)/2 = 4/2 = 2
x₂ = ( 6 + 2)/2 = 8/2 = 4
16)
(11 +x)(14+x) =304
11 * 14 +11x + 14x + x² = 304
x² + 25x +154 = 304
x² + 25x +154 - 304 =0
x² + 25x - 150 = 0
D = 25² - 4*1*(-150) = 625 +600 = 1225 = 35²
x₁ = ( - 25 - 35)/(2*1) = -60/2 = -30
x₂ = (-25 +35)/2 = 10/2 = 5
{a}- ар. пр.
S(6)= (a(1) + a(5))/2 * 5=
a(5)= a(1) + 4 d
d=a(2) - a(1) = -1.2 - (-6.2) = 5
a(5)= -6.2 + 4*5 = 13.8
S(6)= (-6.2 + 13.8.)/2 *5= (7.6/2)*5= 19
36а²-1-(36а²+12а-15а-5)=36а²-1-36а²-12а+15а+5=3а+4
при а=0,2
3*0,2=0,6+4=4,6
<span>(3-¹) -³ (перемножаем степени), получается 3^3= 9*3= 27</span>
