How do I solve this?

Mathematics

1 answer:

ch4aika [34]3 years ago

4 0

Answer:

$x = \frac{3}{2} + \frac{ \sqrt{5} }{2} ; \: \: x = \frac{3}{2} - \frac{ \sqrt{5} }{2}$

Step-by-step explanation:

$1 + \frac{1}{ {x}^{2} } = \frac{3}{x} \\ \\ \frac{ {x}^{2} + 1 }{ {x}^{2} } = \frac{3}{x} \\ \\ {x}^{2} + 1 = \frac{3 {x}^{2} }{x} \\ \\ {x}^{2} + 1 = 3x \\ \\ {x}^{2} - 3x + 1 = 0 \\ equating \: it \: with \\ a {x}^{2} + bx + c = 0 \\ a = 1 \\ b = - 3 \\ c = 1 \\ \\ x = \frac{ - b \pm \sqrt{ {b}^{2} - 4ac} }{2a} \\ \\ x = \frac{ - ( - 3) \pm \sqrt{ {( - 3)}^{2} - 4 \times 1 \times 1} }{2 \times 1} \\ \\ x = \frac{ 3 \pm \sqrt{ {9 - 4}} }{2} \\ \\ x = \frac{ 3 \pm \sqrt{ {5}} }{2} \\ \\ x = \frac{3}{2} + \frac{ \sqrt{5} }{2} ; \: \: x = \frac{3}{2} - \frac{ \sqrt{5} }{2}$

You might be interested in

What is the outlier set of data for 10,12,19,23,26,26,27,34,40?

NikAS [45]

Answer:

In this set of data there is no outlier, as all numbers are relatively close.

4 0

3 years ago

Write each equation in standard form. identify A,B,C.

aleksley [76]

Write in y=ax²+bx+c form
solve for y

given
$\frac{x+5}{3}=-2y+4$
solve for y

easy
minus 4 both sides
$\frac{x+5}{3}-4=-2y$
times -1/2 to both sides
$\frac{x+5}{-6}+2=y$
$y=\frac{x+5}{-6}+2$
$y=\frac{-x}{6}-\frac{6}{5}+2$
2=10/5
$y=\frac{-1}{6}x-\frac{6}{5}+\frac{10}{5}$
$y=\frac{-1}{6}x+\frac{4}{5}$
y=ax²+bx+c
$y=0x^2+\frac{-1}{6}x+\frac{4}{5}$

a=0
b= $\frac{-1}{6}$
c= $\frac{4}{5}$

3 0

3 years ago

Two pounds of dried cranberries call $5.04 , 3 pounds of dried cranberries cost $7.56, and 7 pounds of dried cranberries cost $1

vivado [14]

The answer is B. Each lb of cranberries is 2.52
Hope this helps!

8 0

3 years ago

Read 2 more answers

Graph the system of equations. Then determine whether the system has no solution, one solution, or infinitely many solutions. If

pav-90 [236]

Answer:

Second option: One solution. Independent.