All categories

3 years ago

Solve the equation x^4+7x^2-18=0 and express each solution in a+bi form

Mathematics

1 answer:

maw [93]3 years ago

4 0

Answer:

The following are the solutions found for x:

+√2 + 0i

-√2 + 0i

0 + 3i

0 - 3i

Step-by-step explanation:

The given equation is:

x⁴ + 7x² - 18 = 0

Rewrite x4 as (x²)²

(x²)² + 7x² − 18 = 0

Let u = x²

u² + 7u − 18 = 0

Factorize:

u² + 9u - 2u - 18 = 0

u(u+9) -2(u+9) = 0

(u-2)(u+9) = 0

(x²-2)(x²+9) = 0

Seperate both equations:

x² - 2 = 0 x² + 9 = 0

x = ±√2 x = ±√-9

x = ±√2 x = ± 3√-1

x = ±√2 + 0i x = 0 ± 3i

You might be interested in

Will mark brainlest how to multipy it

Lesechka [4]

Answer:

$\displaystyle x = 2 \sqrt{3}$

Step-by-step explanation:

we would like to solve the following equation:

$\displaystyle \sqrt{3} = \frac{6}{x}$

in order to do so do cross multiplication:

$\displaystyle x \sqrt{3} = 6$

divide both sides by √3:

$\displaystyle x = \frac{6}{ \sqrt{3}}$

since we ended up with a square root on the denominator so we can consider rationalising the denominator to do so multiply both numerator and denominator by √3 which yields:

$\displaystyle x = \frac{6}{ \sqrt{3}} \times \frac{ \sqrt{3} }{ \sqrt{ 3} }$

simplify multiplication:

$\displaystyle x = \frac{6 \sqrt{3} }{ 3}$

reduce fraction:

$\displaystyle x = 2 \sqrt{3}$

and we are done!

6 0

3 years ago

Help! Will mark brainliest!

miss Akunina [59]

Answer: a rise of 12 and a run of 7

Step-by-step explanation:

7 0

2 years ago

adam bought a box of fruit that weighed 6 1/4 pounds. if he bought a second box that weighed 8 1/8 pounds , what is the combined

Serhud [2]

Answer:

14 3/8 pounds

Step-by-step explanation:

6 pounds plus 8 pounds= 14 pounds. 1/4 + 1/8= 3/8. 1/4 can be turned into 2/8, and 2/8 plus 1/8 equals 3/8. Hope this helps :)

3 0

3 years ago

A farmer is building a grain silo for storage. he estimates that will need 256 cubic yards of storage. the grain silo will be sh

Vlad1618 [11]

Check the picture below.

keeping in mind that a cube is just a rectangular prism with all equal sides.

7 0

3 years ago

The probability of an event not happening is

Stels [109]

the probability of an event occurring, it is easy to compute the probability that the event does not occur. If P(A) is the probability of Event A, then 1 - P(A) is the probability that the event does not occur. For the last example, the probability that the total is 6 is 5/36.

3 0

3 years ago