Question

2. Qual é o conjunto solução de cada uma das seguintes equações do 2° grau, sendo U = R?

a) x² + 3x (x - 12) = 0

b) (x - 5)² = 25 - 9x

c) (x - 4)² + 5x(x - 1) = 16​

Answer 1

Resposta:

-a) x² +3x ×(x -12)= 0

x² +3x² -36x= 0

4x² -36x= 0

x² -9x= 0

Δ= (-9)² -4×1×0

Δ= 81

x= \frac{9 +-9}{2}

2

9+−9

x'= \frac{18}{2}

2

18

= 9 x"= \frac{0}{2}

2

0

= 0

B) (x -5)²= 25 -9x

x² -10x +25= 25 -9x

x² -x = 0

Δ= (-1)² -4×1×0

Δ= 1

x= \frac{1 +-1}{2}

2

1+−1

x'= \frac{2}{2}

2

2

= 1 x"= \frac{0}{2}

2

0

= 0

C) (x -4)² + 5x ×(x -1)= 16

x² -8x +16 +5x² -5x= 16

6x² -13x= 0

Δ= (-13)² -4×6×0

Δ= 169

x= \frac{13+-13}{2.6}

2.6

13+−13

x'= \frac{26}{12}_{:2} ^{:2} =\frac{13}{6}

12

26

:2

:2

=

6

13

x"= \frac{0}{12}

12

0

= 0

3-A) x² -2x= 2x -4

x² +4= 0

Δ= 0² -4×1×4

Δ= -16

Δ=∅

B) x² -2x= x +4

x² -3x -4

Δ= (-3)² -4×1×(-4)

Δ= 9 +16

Δ= 25

x= \frac{3 +-5}{2}

2

3+−5

x'= \frac{8}{2}

2

8

= 4 x"= -\frac{2}{2}−

2

2

= -1

C) 6x² +3x= 1 +2x

6x² +x -1

Δ= 1² -4×6× (-1)

Δ= 1 +24

Δ= 25

x= \frac{-1+-5}{2.6}

2.6

−1+−5

x'= \frac{4}{12} =\frac{1}{3}

12

4

=

3

1

x"= -\frac{6}{12}=-\frac{1}{2}−

12

6

=−

2

1

D) 9x² +3x +1= 4x²

5x² +3x +1=

Δ= 3² -4×5×1

Δ= 9 -20

Δ= -11

Δ=∅