Question

Решите1(x-2'5) -4 1/5 = 6,3/(x-2,5)2) 3,5*(x+2 1/4 5) = 14​

Answer 1

1) (x-2,5) -4(1/5) = 6,3/(x-2,5)|×(х-2,5)

так как на ноль делить нельзя:

(х-2,5)≠0
х≠2,5

(х-2,5)(х-2,5)=(х-2,5)²

4(1/5)=4,2

(х-2,5)²-4,2(х-2,5)=6,3(х-2,5)/(х-2,5)

х²-5х+6,25-4,2х+10,5=6,3

х²-9,2х+16,75-6,3=0

х²-9,2х+10,45=0

D²=(-(-9,2))²-4×1×10,45=84,64-41,8=42,84

x1=(-(-9,2)-√42,84/2×1|√42,84=6,545|=(9,2-6,545)/2=2,655/2=1,3275≈1,33

x2=(-(-9,2)+√42,84)/2×1=(9,2+6,545)/2=15,745/2=7,8725≈7,87

Проверка:

(1,33-2,5)-4,2=6,3/(1,33-2,5)

-1,17-4,2=6,3/(-1,17)

(-5,37)=(-5,38)

(-5,4)=(-5,4)-истина

(7,87-2,5)-4,2=6,3/(7,87-2,5)

5,37-4,2=6,3/5,37

1,17=1,173|1,173≈1,17

1,17=1,17-истина

Ответ: Оба корня, х1=1,33 и х2=7,87, являются нашим решением. Так как удовлетворяют нашему условию х≠2,5


2) 3,5*(x+2(1/45)) =14|÷3,5

х+2(1/45)=4

2(1/45)=(91/45)

х=4-(91/45)

х=(4×45-91)/45

х=(180-91)/45

х=(89/45)

х=1(44/45)

Проверка:

3,5(1(44/45)+2(1/45))=14

3,5×4=14

14=14-истина.

Ответ: х=1(44/45)

Answer 2

To solve the equations, I'll perform the necessary steps for each equation:

1. (x - 2.5) - 4(1/5) = 6.3 / (x - 2.5)^2

Step 1: Clear the fraction by multiplying everything by 5(x - 2.5)^2: 5(x - 2.5)(x - 2.5) - 4(1) = 6.3

Step 2: Expand and simplify: 5(x^2 - 5x + 6.25) - 4 = 6.3

Step 3: Distribute the 5: 5x^2 - 25x + 31.25 - 4 = 6.3

Step 4: Combine like terms: 5x^2 - 25x + 27.25 = 6.3

Step 5: Move all terms to one side of the equation: 5x^2 - 25x + 27.25 - 6.3 = 0

Step 6: Combine constants: 5x^2 - 25x + 20.95 = 0

Step 7: Now, we can solve this quadratic equation. However, it appears that the equation doesn't have real solutions. The discriminant (b^2 - 4ac) is negative, indicating that the solutions are complex. Thus, the solution to this equation is a complex solution, but we can't provide a real solution.

2. 3.5 * (x + 2.25) = 14

Step 1: Divide both sides by 3.5 to isolate the variable: x + 2.25 = 14 / 3.5

Step 2: Simplify the right side: x + 2.25 = 4

Step 3: Move 2.25 to the other side of the equation: x = 4 - 2.25

Step 4: Calculate the result: x = 1.75

The solution to the second equation is x = 1.75.