Question

Factorize 21x^2 - 16-7x / 3x^2-4 = 5

Answer 1

Answer:
`\bold{(12x - 7 - i√(47))(12x - 7 + i√(47))=0}`

Explanation:

`(21x^2-7x - 16)/(3x^2-4)=5`

cross multiply: 21x² - 7x - 16 = 15x² - 20

set equal to 0: 6x² - 7x + 4 = 0

Use quadratic formula to find the roots:

a=6, b=-7, c=4

`x=(-b \pm √(b^2-4ac))/(2a)`

`=(-(-7) \pm √((-7)^2-4(6)(4)))/(2(6))`

`=(7 \pm √(49-96))/(12)`

`=(7 \pm √(-47))/(12)`

`=(7 \pm i√(47))/(12)`

`x_1 =(7 + i√(47))/(12) \qquad >>\qquad (12x - 7 - i√(47))= 0`

`x_2 =(7 - i√(47))/(12) \qquad >>\qquad (12x - 7 + i√(47))= 0`