Question

2x²-5x-3=0 3x²+16x-12=0 4x²+8a-32=0

Answer 1

V-квадратный корень
2x²-5x-3=0

D=(-(-5))^2-4×2×(-3)=25-(-24)=25+24=49

x1=(-(-5)-V49)/2×2=(5-7)/4=-2/4=-1/2
x2=(-(-5)+V49)/2×2=(5+7)/4=12/4=3

3x²+16x-12=0
D=(-16)^2-4×3×(-12)=256-(-144)=256+144=400
x1=(-16-V400)/2×3=(-16-20)/6=-36/6=-6
x2=(-16+V400)/2×6=(-16+20)/6=4/6=2/3

4x²+8a-32=0
4x^2=32-8a
4x^2=4(8-2a)|:4
x^2=(8-2a)

x1=-V(8-2a)
x2=V(8-2a)

Answer 2

To solve each of these quadratic equations, we can use the quadratic formula:

For a quadratic equation of the form ax²+bx+c=0, the solutions are given by:

x = (-b ± sqrt(b²-4ac)) / 2a

Using this formula, we can solve each of the quadratic equations you provided:

1. 2x²-5x-3=0:

a = 2, b = -5, c = -3

x = (-(-5) ± sqrt((-5)²-4(2)(-3))) / 2(2)

x = (5 ± sqrt(25+24)) / 4

x = (5 ± sqrt(49)) / 4

x = (5 ± 7) / 4

x1 = 3, x2 = -1/2

Therefore, the solutions to this equation are x = 3 and x = -1/2.

2. 3x²+16x-12=0:

a = 3, b = 16, c = -12

x = (-16 ± sqrt(16²-4(3)(-12))) / 2(3)

x = (-16 ± sqrt(256+144)) / 6

x = (-16 ± sqrt(400)) / 6

x1 = (-16 + 20) / 6 = 2/3, x2 = (-16 - 20) / 6 = -2

Therefore, the solutions to this equation are x = 2/3 and x = -2.

3. 4x²+8a-32=0:

a = 8a-32=0, which can be simplified to a-4=0. So a = 4.

a = 4, b = 0, c = -32

x = (-(0) ± sqrt(0²-4(4)(-32))) / 2(4)

x = (0 ± sqrt(512)) / 8

x1 = sqrt(512) / 8 = sqrt(64*2) / 8 = 4sqrt(2) / 8 = sqrt(2) / 2

x2 = -sqrt(512) / 8 = -sqrt(2) / 2

Therefore, the solutions to this equation are x = sqrt(2) / 2 and x = -sqrt(2) / 2.