Question

determine as raízes da equação x2+2/3×+1/9= 4/25

Answer 1

x² + 2x/3 + 1/9 = 4/25

x² + 2x/3 + 1/9 - 4/25 = 0

(225x² + 75.2x + 25.1 - 9.4)/225 = 0/225

225x² + 150x + 25 - 36 = 0

225x² + 150x - 9 = 0 (:3)

75x² + 50x - 3 = 0

a = 75; b = 50;c = - 3

Δ = b² - 4ac

Δ = 50² - 4.75.(-3)

Δ = 2500 + 300.3

Δ = 2500 + 900

Δ = 3600

X = [ - b +/- √Δ]/2a

A = 75; B = 50; C = - 3

X = [ - 50 +/- √3600]/2.75

x' = [ - 50 - 60]/150 = - 110/150 = - 11/15

x" = [ - 50 + 60]/150 = 10/150 = 1/15

R.: x' = -11/15 ; x" = 1/15

mmc (3,9,25) = 225

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

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       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

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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