Question

Resolva a equação x 2 − 6x − 7 = 0 no conjunto IR.

Answer 1

Resposta:

\begin{gathered}x^2+6x-7=0 \\ \\ \Delta = b^2-4*a*c \\ \Delta = 6^2-4*1*(-7) \\ \Delta = 36+28 \\ \Delta = 64 \\ \\ x_1 = \dfrac{-b+ \sqrt{\Delta} }{2*a} = \dfrac{-6+ \sqrt{64} }{2*1} = \dfrac{-6+8}{2} = \dfrac{2}{2} = 1 \\ \\ \\ x_2 = \dfrac{-b- \sqrt{\Delta} }{2*a} = \dfrac{-6- \sqrt{64} }{2*1} = \dfrac{-6-8}{2} = \dfrac{-14}{2} = -7\end{gathered}

x

2

+6x−7=0

Δ=b

2

−4∗a∗c

Δ=6

2

−4∗1∗(−7)

Δ=36+28

Δ=64

x

1

=

2∗a

−b+

Δ

=

2∗1

−6+

64

=

2

−6+8

=

2

2

=1

x

2

=

2∗a

−b−

Δ

=

2∗1

−6−

64

=

2

−6−8

=

2

−14

=−7

Solução: (-7, 1)