Question

Помогите с уравнениями: а) 2х^2+9х+4=0; b) одна шестая х^2- тринадцать х шестых + 7=0; в) 19х2-76=0; г) две целых одна третья х^2- три одна вторая х= 0; где письмено писал это дробью надо записать

Answer 1

А)2x^2 +9x +4 =0;
D= 81-32=49=7^2;
 x1= -4;  x2= - 1/2.
б)  x^2/6 + 13x /6 + 7=0;  /*6;
x^2 +13x +42 =0;
 D=169-168=1=1^2;
x1= - 7; x2 =  - 6.
в) 19x^2 =76;
x^2 =4;
x1= -2; x2 =2.
г) 7x^2 /3 - 7x /2 =0;   /*6;
14x^2 - 21x=0;
x(14x -21)=0;
 x1=0; x2=1,5

Answer 2

Solving Equations:

Let's solve the given equations step by step:

a) 2x^2 + 9x + 4 = 0

b) (1/6)x^2 - 13x + (7/6) = 0

c) 19x^2 - 76 = 0

d) (2 + 1/3)x^2 - (3 + 1/2)x = 0

Solution:

a) To solve the equation 2x^2 + 9x + 4 = 0, we can use the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 2, b = 9, and c = 4. Plugging these values into the quadratic formula, we get:

x = (-9 ± √(9^2 - 4 * 2 * 4)) / (2 * 2)

Simplifying further:

x = (-9 ± √(81 - 32)) / 4

x = (-9 ± √49) / 4

x = (-9 ± 7) / 4

So, the solutions to the equation 2x^2 + 9x + 4 = 0 are:

x = (-9 + 7) / 4 = -1/2

x = (-9 - 7) / 4 = -4

b) To solve the equation (1/6)x^2 - 13x + (7/6) = 0, we can multiply the entire equation by 6 to eliminate the fractions:

x^2 - 78x + 7 = 0

Unfortunately, this equation does not factor easily. We can use the quadratic formula to find the solutions:

x = (-(-78) ± √((-78)^2 - 4 * 1 * 7)) / (2 * 1)

Simplifying further:

x = (78 ± √(6084 - 28)) / 2

x = (78 ± √6056) / 2

x = (78 ± 77.85) / 2

So, the solutions to the equation (1/6)x^2 - 13x + (7/6) = 0 are approximately:

x ≈ 0.15

x ≈ 77.85

c) To solve the equation 19x^2 - 76 = 0, we can rearrange the equation to isolate x:

19x^2 = 76

x^2 = 76/19

Taking the square root of both sides:

x = ±√(76/19)

Simplifying further:

x = ±√(4) ≈ ±2

So, the solutions to the equation 19x^2 - 76 = 0 are:

x ≈ 2

x ≈ -2

d) To solve the equation (2 + 1/3)x^2 - (3 + 1/2)x = 0, we can multiply the entire equation by 6 to eliminate the fractions:

6(2 + 1/3)x^2 - 6(3 + 1/2)x = 0

Simplifying further:

6(2 + 1/3)x^2 - 6(3 + 1/2)x = 0

18x^2 - 36x - 9x + 18 = 0

18x^2 - 45x + 18 = 0

Unfortunately, this equation does not factor easily. We can use the quadratic formula to find the solutions:

x = (-(-45) ± √((-45)^2 - 4 * 18 * 18)) / (2 * 18)

Simplifying further:

x = (45 ± √(2025 - 1296)) / 36

x = (45 ± √729) / 36

x = (45 ± 27) / 36

So, the solutions to the equation (2 + 1/3)x^2 - (3 + 1/2)x = 0 are:

x = (45 + 27) / 36 = 4/3

x = (45 - 27) / 36 = 6/3 = 2

Therefore, the solutions to the given equations are as follows:

a) 2x^2 + 9x + 4 = 0: - x = -1/2 - x = -4

b) (1/6)x^2 - 13x + (7/6) = 0: - x ≈ 0.15 - x ≈ 77.85

c) 19x^2 - 76 = 0: - x ≈ 2 - x ≈ -2

d) (2 + 1/3)x^2 - (3 + 1/2)x = 0: - x = 4/3 - x = 2