Question

Descubra quais são as raízes da equação x2+2/3x+1/9=4/25

Answer 1

x² + 2x + 1  = 4 
       3      9    25

mmc (3,9,25) = 225

225x² + 150x + 25 = 36
        225                 225

225x² + 150x + 25 = 36
225x² + 150x + 25 - 36 = 0
225x² + 150x - 11 = 0

a = 225; b = 150; c = - 11

Δ = b² - 4ac
Δ = 150² - 4.225.(-11)
Δ = 22500 - 900.(-11)
Δ = 22500 + 9900
Δ = 32400
√Δ = 180

x = - b +/- √Δ = - 150 +/- √32400
          2a                2.225

x = - 150 + 180 =  30   (:30)  =  1
            450          450  (:30)     15

x = - 150 - 180 = - 330  (: 30)  = - 11
           450           450   (:30)       15

Resp.: 1/15 e - 11/15
=============================
mmc:

3,9,25: 3
1,3,25: 3
1,1,25: 5
1,1,5: 5
1,1,1     = 3.3.5.5 = 9.25 = 225

Answer 2

x² + 2x + 1  = 4 

      3      9    25

mmc (3,9,25) = 225

225x² + 150x + 25 = 36

----------------------------------------

       225                 225

225x² + 150x + 25 = 36

225x² + 150x + 25 - 36 = 0

225x² + 150x - 11 = 0

a = 225; b = 150; c = - 11

Δ = b² - 4ac

Δ = 150² - 4.225.(-11)

Δ = 22500 - 900.(-11)

Δ = 22500 + 9900

Δ = 32400

√Δ = 180

x = - b +/- √Δ = - 150 +/- √32400

         2a                2.225

x = - 150 + 180 =  30   (:30)  =  1

           450          450  (:30)     15

x = - 150 - 180 = - 330  (: 30)  = - 11

          450           450   (:30)       15

Resp.: 1/15 e - 11/15

=============================

mmc:

3,9,25: 3

1,3,25: 3

1,1,25: 5

1,1,5: 5

1,1,1     = 3.3.5.5 = 9.25 = 225