Just a quick question.

What is a simple way to solve for the sum and difference of 2 cubes? For example, 27+64<img src="https://tex.z-dn.net/?f=x%5E3"

salantis [7]

Answer:

(3 + 4x)(9 - 12x + 16x²) = 0

(4m - 1)(16m² + 4m + 1) = 0

Step-by-step explanation:

Here we have to solve the sum of two cubes which is $27 + 64x^{3}$

Now, the equation is $27 + 64x^{3} = 0$

⇒ 3³ + (4x)³ = 0

⇒ (3 + 4x)[3² - 3(4x) + (4x)²] = 0

⇒ (3 + 4x)(9 - 12x + 16x²) = 0

So, (3 + 4x) = 0 or (9 - 12x + 16x²) = 0

Therefore, from the above two relation we can solve for x.

One root will be $- \frac{3}{4}$ and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation.

Again, we have to solve the difference of two cubes which is $64m^{3} - 1$

Now, the equation is $64m^{3} - 1 = 0$

⇒ (4m)³ - 1³ = 0

⇒ (4m - 1)[(4m)² + 4m(1) + 1²] = 0

⇒ (4m - 1)(16m² + 4m + 1) = 0

So, (4m - 1) = 0 or (16m² + 4m + 1) = 0

Therefore, from the above two relation we can solve for m.

One root will be $\frac{1}{4}$ and the others we will get by applying Sridhar Acharya Formula, which will give a pair of conjugate imaginary roots of the equation. (Answer)

8 0

2 years ago

1. A man has 5 grandchildren, 4 girls and 1 boy. He thinks this is unusual. If the probability that any child born

mojhsa [17]

Answer:

6.25%

Step-by-step explanation:

To know the final probability that this has happened, we must multiply the probability of each event, they tell us that the probability that it is a girl is 1/2 and this happened 4 times, therefore:

(1/2) ^ 4 = 0.0625

that is, the probability that 4 girls are born is 6.25%

an unusual probability is considered when it is less than 5%, therefore, although it approaches this figure, it is not unusual

4 0

2 years ago

When Zack checked his solution, it didn’t work. What was his mistake?

KatRina [158]

Answer:

he whent up and not down and left and not right

Step-by-step explanation:we just is messed up in life

4 0

2 years ago

Read 2 more answers

PLLLLLLLZZZZZZZZZZZZZZZ Help Me In the diagram, ZY = WX = 2 StartRoot 10 EndRoot. What is the perimeter of rectangle WXYZ? Start

jenyasd209 [6]

Answer:

The Answer Is C

Step-by-step explanation:

4 0

3 years ago

How can you use the order of operation to explain why you cannot combine the variable terms before using the distributive proper

bazaltina [42]

Answer:

Step-by-step explanation:

The Order of Operations is very important when simplifying expressions and equations. The Order of Operations is a standard that defines the order in which you should simplify different operations such as addition, subtraction, multiplication and division.

This standard is critical to simplifying and solving different algebra problems. Without it, two different people may interpret an equation or expression in different ways and come up with different answers. The Order of Operations is shown below.

Parentheses and Brackets -- Simplify the inside of parentheses and brackets before you deal with the exponent (if any) of the set of parentheses or remove the parentheses.

Exponents -- Simplify the exponent of a number or of a set of parentheses before you multiply, divide, add, or subtract it.

Multiplication and Division -- Simplify multiplication and division in the order that they appear from left to right.

Addition and Subtraction -- Simplify addition and subtraction in the order that they appear from left to right.

Before we begin simplifying problems using the Order of Operations, let's examine how failure to use the Order of Operations can result in a wrong answer to a problem.

Without the Order of Operations one might decide to simplify the problem working left to right. He or she would add two and five to get seven, then multiply seven by x to get a final answer of 7x. Another person might decide to make the problem a little easier by multiplying first. He or she would have first multiplied 5 by x to get 5x and then found that you can't add 2 and 5x so his or her final answer would be 2 + 5x. Without a standard like the Order of Operations, a problem can be interpreted many different ways

7 0

2 years ago