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3 years ago

WILL GIVE BRAINLIEST

Mathematics

1 answer:

kakasveta [241]3 years ago

6 0

Answer:

116 seats 6+5*22

Step-by-step explanation:

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What are the solutions of the equation x6 + 6x3 + 5 = 0? Use factoring to solve.

lapo4ka [179]

Consider the equation $x^6+6x^3+5=0$ .

First, you can use the substitution $t=x^3$ , then $x^6=(x^3)^2=t^2$ and equation becomes $t^2+6t+5=0$ . This equation is quadratic, so

$D=6^2-4\cdot 5\cdot 1=36-20=16=4^2,\ \sqrt{D}=4,\\ \\ t_{1,2}=\dfrac{-6\pm 4}{2} =-5,-1$ .

Then you can factor this equation:

$(t+5)(t+1)=0$ .

Use the made substitution again:

$(x^3+5)(x^3+1)=0$ .

You have in each brackets the expression like $a^3+b^3$ that is equal to $(a+b)(a^2-ab+b^2)$ . Thus,

$x^3+5=(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25}) ,\\x^3+1=(x+1)(x^2-x+1)$

and the equation is

$(x+\sqrt[3]{5})(x^2-\sqrt[3]{5}x+\sqrt[3]{25})(x+1)(x^2-x+1)=0$ .

Here $x_1=-\sqrt[3]{5} , x_2=-1$ and you can sheck whether quadratic trinomials have real roots:

1. $D_1=(-\sqrt[3]{5}) ^2-4\cdot \sqrt[3]{25}=\sqrt[3]{25} -4\sqrt[3]{25} =-3\sqrt[3]{25}$ .

2. $D_2=(-1)^2-4\cdot 1=1-4=-3$ .

This means that quadratic trinomials don't have real roots.

Answer: $x_1=-\sqrt[3]{5} , x_2=-1$

If you need complex roots, then

$x_{3,4}=\dfrac{\sqrt[3]{5}\pm i\sqrt{3\sqrt[3]{25}}}{2} ,\\ \\x_{5,6}=\dfrac{1\pm i\sqrt{3}}{2}$ .

6 0

4 years ago

Reese is selling lemonade at the parade. He gets to keep 50% of the money he collects. A large lemonade is $6.00 and a small lem

yuradex [85]

Answer:

Step-by-step explanation:

Given data

We are given that

Large lemonade= $6

Small lemonade= $4

Total amount = 6+4= $10

He keeps 50% of the total

= 50/100*10

=0.5*10

= $5

Hence he will keep $5

8 0

3 years ago

Choose the expression that represents "three less

Anna35 [415]

Answer:

none of your options are right

Step-by-step explanation:

<h2>Three less than seven times a number:</h2>

three : 3, less than : (-), seven : 7, times : (multiplication symbol), a number : (x)

the answer is : 3 - 7 (x)

: 3-7x

5 0

2 years ago

Which of the following is the conjugate of a complex number with 2 as the real part and −8 as the imaginary part?

vampirchik [111]

The complex number is given as: 2-8i

So for conjugate, you just flip the sign of the imaginary part:

2+8i will be the answer

3 0

3 years ago

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1. Taylor drinks 2 liters of water during

cestrela7 [59]

Answer:

4000 Milliliters......

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3 years ago