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SVETLANKA909090 [29]
3 years ago
8

Hi. Please I need help with these questions.

Mathematics
1 answer:
VashaNatasha [74]3 years ago
4 0

9514 1404 393

Answer:

  21x² +20x +100 = 0

Step-by-step explanation:

We know the sum of the roots of x² +bx +c = 0 is -b, and their product is c. If the roots are α and β, then ...

  • α+β = -b
  • αβ = c

The sum of the roots of the new equation will be ...

  -b' = (α+1/β)+(β+1/α) = (α+β) +(1/α +1/β) = (α+β)(1 +1/(αβ))

The product of the roots of the new equation will be ...

  c' = (α+1/β)(β+1/α) = αβ +2 +1/(αβ)

Using the above relations for (α+β) and αβ, we find that ...

  -b' = (-b)(1 +1/c)

  c' = c + 2 + 1/c

For the given equation, our definition of b and c is ...

  b = 2/3

  c = 7/3

so the new equation has values ...

  b' = (2/3)(1 + 1/(7/3) = (2/3)(10/7) = 20/21

  c' = 7/3 + 2 + 1/(7/3) = 13/3 + 3/7 = 100/21

So, the equation with the roots of interest is ...

  x² +20/21x +100/21 = 0

Multiplying by 21 gives ...

  21x² +20x +100 = 0

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3 years ago
The elimination method is ideal for solving this system of equations. By which number must you multiply the second equation to e
shutvik [7]

Given:

The system of equations is

x+3y=42       ...(i)

2x-y=14        ...(ii)

To find:

The number that must be multiplied with the second equation to eliminate the y-variable.

Solution:

Coefficient of y variable in equation (i) is 3 and in equation (ii) is -1.

To eliminate y-variable the absolute value of coefficients of y-variables should be same.

So, we need to multiply the second equation by 3 to eliminate the y-variable

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Adding (i) and (iii), we get

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Divide both sides by 7.

x=12

Put x=12 in (i).

12+3y=42

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Divide both sides by 10.

y=10

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7 0
3 years ago
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