Question

URGENTE !!!

escreva as equações na forma reduzida e, sem resolve-las, determine a soma S e o produto P das raízes de cada uma

a) x-1 / 4 = 5 / x-2

b) 1 / x+1 / x+1 = 5 / 6

c) x / x-2 + 4 / x-1 = 5​

Answer 1

Resposta:

a.

\dfrac{x - 1}{4} = \dfrac{5}{x - 2}

4

x−1

=

x−2

5

20 = x^2 - 2x - x + 220=x

2

−2x−x+2

x^2 - 3x - 18 = 0x

2

−3x−18=0

x' + x'' = 3x

′

+x

′′

=3

x'.x'' = -18x

′

.x

′′

=−18

b.

\dfrac{\dfrac{1}{x + 1}}{x + 1} = \dfrac{5}{6}

x+1

x+1

1

=

6

5

\dfrac{1}{(x + 1)^2} = \dfrac{5}{6}

(x+1)

2

1

=

6

5

\dfrac{1}{(x^2 + 2x + 1)} = \dfrac{5}{6}

(x

2

+2x+1)

1

=

6

5

5x^2 + 10x -1 = 05x

2

+10x−1=0

x' + x'' = -2x

′

+x

′′

=−2

x'.x'' = -\dfrac{1}{5}x

′

.x

′′

=−

5

1

c.

\dfrac{x}{x - 2} + \dfrac{4}{x - 1} = 5

x−2

x

+

x−1

4

=5

x(x - 1) + 4(x - 2) = 5(x - 2)(x - 1)x(x−1)+4(x−2)=5(x−2)(x−1)

x^2 + 3x - 8 = 5x^2 - 15x + 10x

2

+3x−8=5x

2

−15x+10

4x^2 - 18x + 18 = 04x

2

−18x+18=0

x' + x'' = \dfrac{9}{2}x

′

+x

′′

=

2

9

x'.x'' = \dfrac{9}{2}x

′

.x

′′

=

2

9