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lina2011 [118]
3 years ago
13

What are the solutions to the equation? x^3 - 8x^2 - x + 8 =0

Mathematics
2 answers:
kogti [31]3 years ago
8 0

Answer:

Step-by-step explanation:

x^3 - 8x² - x + 8 =0

x^3 - 8x² - (x - 8 )=0

x²(x-8) - (x-8) = 0

(x-8)(x² -1) =0

x-8 = 0  or x² - 1 = 0

x-8=0 or (x-1)(x+1)=0

x=8 x=1 or x=-1

raketka [301]3 years ago
3 0

<u>ANSWER:  </u>

The solutions of the x^{3}-8 x^{2}-x+8=0 is -1, 1, 8

<u>SOLUTION: </u>

Given, cubic equation is x^{3}-8 x^{2}-x+8=0 --- eqn 1

We need to find the solutions of the given cubic equation.

When we observe the equation clearly, we can notice that sum of coefficients is zero

According to polynomial identities, we can say that 1 is one of its solutions.

Let, a,b,c be the solutions of any equation, then its general form is  

x^{3}-(a+b+c) x^{2}+(a b+b c+c a) x+a b c=0 --- eqn (2)

On comparing both (1) and (2)

a + b + c = 8, ab +bc + ca = -1, abc = -8

We know, one solution is 1, let it be c, i.e. c=1

a + b + 1 = 8, ab + b +a = -1, ab = -8

We can conclude that a + b = 7, ab = -8, from above three equations

We know that, (a-b)^{2}=(a+b)^{2}-4 a b

(a-b)^{2}=7^{2}-4 \times(-8)

(a-b)^{2}=49+32

(a-b)^{2}=81

(a-b)=9

add (a + b) and (a – b) we get  

a+ b + a-b = 7 + 9

2a = 16

a = 8

Substitute a value in a+b =7 , we get

8 + b =7

b =-1

Hence, the solutions of the x^{3}-8 x^{2}-x+8=0 is -1 , 1 , 8

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Step-by-step explanation:

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Karim began his day by drinking 1 cups of milk at breakfast. By the end of the day, he drank a total of 2
uranmaximum [27]

Answer:

Equation:

21 = 1 + m

Solution:

20 = m

Step-by-step explanation:

What we know:

  • Karim drank 1 cup of milk at breakfast
  • Karim drank a total of 21 cups of milk
  • m = the amount of milk, in cups, Karim drank after breakfast

We know that Karim drank 21 cups of milk in a day. In an equation, that would look like this:

21 =

What does 21 equal?

The amount of milk Karim drank at breakfast plus the amount of milk Karim drank after breakfast.

21 = milk at breakfast + milk after breakfast

Let's substitute what we know into this equation:

21 = milk at breakfast + milk after breakfast

21 = 1 + m

Now that we have our equation, let's solve.

21 = 1 + m

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Therefore, Karim drank 20 cups of milk after breakfast.

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3 years ago
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solniwko [45]

Answer:

11.91

Step-by-step explanation:

The question says there is a new line that connects V and T. If this line is drawn, the diagram would have a right-angle triangle. This triangle is called TUV.

In triangle TUV, the side length created by the points VT is the hypotenuse.

For right-angle triangles, you can use the Pythagorean theorem to find any side.

It's in the format side² + side² = hypotenuse².

To use the formula, you need to know the length of the other two sides. The length of these sides, because they are exactly horizontal or vertical, is found by subtracting the smaller coordinate from the other (that is not the same).

The lengths of other sides:

VU:

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UT:

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