Equação Exponencial 1.docx
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1) Resolver a equação exponencial abaixo 𝑋
𝑋
(√5 + 2√6) + (√5 − 2√6) = 10 𝑋
𝑎 = (√5 + 2√6)
√5+2√6 Segue que√5 − 2√6 = √5 − 2√6. √5+2√6
√52 −(2√6)2
√5 − 2√6=
√5+2√6
=
1 √5+2√6 𝑋
𝑋
1
(√5 − 2√6) = (
√5 + 2√6
)
1
𝑎 + = 10
A equação fica:
𝑎
𝑎2 + 1 = 10𝑎 →
𝑎2 − 10𝑎 + 1 = 0
∆= (−10)2 − 4.1.1= 100 – 4 = 96 → √∆=√96=4√6
𝑎=
10 ± 4√6 = 5 ± 2√6 2 𝑋
1)
(√5 + 2√6) = 5 + 2√6
→X=2
2)
(√5 + 2√6) = 5 − 2√6 =
1 = 5+2√6
Conjunto solução: S = { -2, 2}
−1
(5 + 2√6) → X = -2
𝑋
(√5 + 2√6) + (√5 − 2√6) = 10 𝑋
𝑎 = (√5 + 2√6)
√5+2√6 Segue que√5 − 2√6 = √5 − 2√6. √5+2√6
√52 −(2√6)2
√5 − 2√6=
√5+2√6
=
1 √5+2√6 𝑋
𝑋
1
(√5 − 2√6) = (
√5 + 2√6
)
1
𝑎 + = 10
A equação fica:
𝑎
𝑎2 + 1 = 10𝑎 →
𝑎2 − 10𝑎 + 1 = 0
∆= (−10)2 − 4.1.1= 100 – 4 = 96 → √∆=√96=4√6
𝑎=
10 ± 4√6 = 5 ± 2√6 2 𝑋
1)
(√5 + 2√6) = 5 + 2√6
→X=2
2)
(√5 + 2√6) = 5 − 2√6 =
1 = 5+2√6
Conjunto solução: S = { -2, 2}
−1
(5 + 2√6) → X = -2
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