Question

Please please help me!!

Answer 1

Explanation:

`\displaystyle \\(6)/(x)=12x+1\ \ \ \ \ \ \ \ \ \ x\\eq 0\\\\ Multiply \ both\ parts \ of\ the \ equation\ by \ x\ (x\\eq 0):\\\\(6)/(x)*x=12x*x+1*x\\\\6=12x^2+x\\\\6-6=12x^2+x-6\\\\0=12x^2+x-6\ \ \ \ \ \ \Leftrightarrow\ \ \ \ \ \ 12x^2+x-6=0\\\\12x^2+x-6=0\\\\D=(-b)^2-4ac\\\\a=12\ \ \ \ b=1\ \ \ \ c=-6\\\\Hence\\\\D=(-1)^2-4*12*(-6)\\\\D=1+288\\\\D=289\\\\√(D)=√(289) \\\\D=17\\\\`

`\displaystyle \\x_(1,2)=(-bб√(D) )/(2a) \\\\x_(1,2)=(-1б17)/(2*12 ) \\\\x_1=(-1-17)/(24) \\\\x_1=-(18)/(24)\\\\\displaystyle x_1=-(3)/(4).\\\\x_2=(-1+17)/(24)\\\\x_2=(16)/(24) \\\\x_2=(2)/(3) .`

`\displaystyle \\Answer:\ x_1=-(3)/(4) \ \ \ \ x_2=(2)/(3) .`

Answer 2

x = -
`(3)/(4)` ,
`(2)/(3)`

Explanation:

`(6)/(x)` = 12x + 1

multiply through by x to clear the fraction , x ≠ 0

6 = 12x² + x ( subtract 6 from both sides )

0 = 12x² + x - 6 , that is

12x² + x - 6 = 0 ← in standard form

consider the factors of the product of the coefficient of the x² term and the constant term which sum to give the coefficient of the x- term.

product = 12 × - 6 = - 72 and sum = + 1

the factors are - 8 and + 9

use these factors to split the x- term

12x² - 8x + 9x - 6 = 0 ( factor first/second and third/fourth terms )

4x(3x - 2) + 3(3x - 2) ← factor out (3x - 2) from each term

(3x - 2)(4x + 3) = 0 ← in factored form

equate each factor to zero and solve for x

3x - 2 = 0 ( add 2 to both sides )

3x = 2 ( divide both sides by 3 )

x =
`(2)/(3)`

and

4x + 3 = 0 ( subtract 3 from both sides )

4x = - 3 ( divide both sides by 4 )

x = -
`(3)/(4)`

solutions are x = -
`(3)/(4)` &
`(2)/(3)`