Nilai c - a² - b² adalah - 12. Dimana nilai a, b, dan c adalah 1, 4, dan 5. Nilai dari (3⁷ⁿ)⁵ + (3⁻⁷ⁿ)⁵ adalah 154.451

Penjelasan dengan langkah-langkah:

Diketahui:

• 3⁷ⁿ + 3⁻⁷ⁿ = 11
• 243⁷ⁿ + 243⁻⁷ⁿ = abc
• a < b < c
• a, b, c ∈ Z

Ditanyakan:

• c - a² - b²?

Jawaban:

(a + b)³ = a³ + 3a²b + 3ab² + b³

(3⁷ⁿ + 3⁻⁷ⁿ)³ = (3⁷ⁿ)³ + 3 (3⁷ⁿ)² 3⁻⁷ⁿ + 3 (3⁷ⁿ) (3⁻⁷ⁿ)² + (3⁻⁷ⁿ)³

(3⁷ⁿ)³ + (3⁻⁷ⁿ)³ = (3⁷ⁿ + 3⁻⁷ⁿ)³ - 3 (3⁷ⁿ)² 3⁻⁷ⁿ - 3 (3⁷ⁿ) (3⁻⁷ⁿ)²

(3⁷ⁿ)³ + (3⁻⁷ⁿ)³ = (11)³ - 3 (3⁷ⁿ) - 3 (3⁻⁷ⁿ)

(3⁷ⁿ)³ + (3⁻⁷ⁿ)³ = (11)³ - 3 (3⁷ⁿ + 3⁻⁷ⁿ)

(3⁷ⁿ)³ + (3⁻⁷ⁿ)³ = 1.331 - 3 (11)

(3⁷ⁿ)³ + (3⁻⁷ⁿ)³ = 1.331 - 33

(3⁷ⁿ)³ + (3⁻⁷ⁿ)³ = 1.298

243⁷ⁿ + 243⁻⁷ⁿ = (3⁵)⁷ⁿ + (3⁵)⁻⁷ⁿ = (3⁷ⁿ)⁵ + (3⁻⁷ⁿ)⁵

• (a + b)⁵ = a⁵ + 5a⁴b + 10a³b² + 10a²b³ + 5ab⁴ + b⁵

(3⁷ⁿ + 3⁻⁷ⁿ)⁵ = (3⁷ⁿ)⁵ + 5 (3⁷ⁿ)⁴ (3⁻⁷ⁿ) + 10 (3⁷ⁿ)³ (3⁻⁷ⁿ)² + 10 (3⁷ⁿ)² (3⁻⁷ⁿ)³ + 5 (3⁷ⁿ) (3⁻⁷ⁿ)⁴ + (3⁻⁷ⁿ)⁵

(3⁷ⁿ)⁵ + (3⁻⁷ⁿ)⁵ = (3⁷ⁿ + 3⁻⁷ⁿ)⁵ - 5 (3⁷ⁿ)⁴ (3⁻⁷ⁿ) - 10 (3⁷ⁿ)³ (3⁻⁷ⁿ)²- 10 (3⁷ⁿ)² (3⁻⁷ⁿ)³ - 5 (3⁷ⁿ) (3⁻⁷ⁿ)⁴

(3⁷ⁿ)⁵ + (3⁻⁷ⁿ)⁵ = (3⁷ⁿ + 3⁻⁷ⁿ)⁵ - 5 (3⁷ⁿ)³ - 10 (3⁷ⁿ) - 10 (3⁻⁷ⁿ) - 5 (3⁻⁷ⁿ)³

(3⁷ⁿ)⁵ + (3⁻⁷ⁿ)⁵ = (11)⁵ - 5 (3⁷ⁿ)³ - 5 (3⁻⁷ⁿ)³ - 10 (3⁷ⁿ) - 10 (3⁻⁷ⁿ)

(3⁷ⁿ)⁵ + (3⁻⁷ⁿ)⁵ = (11)⁵ - 5 ((3⁷ⁿ)³ + (3⁻⁷ⁿ)³) - 10 (3⁷ⁿ + 3⁻⁷ⁿ)

(3⁷ⁿ)⁵ + (3⁻⁷ⁿ)⁵ = (11)⁵ - 5 (1.298) - 10 (11)

(3⁷ⁿ)⁵ + (3⁻⁷ⁿ)⁵ = 161.051 - 6.490 - 110

(3⁷ⁿ)⁵ + (3⁻⁷ⁿ)⁵ = 154.451

Info ada kesalahan, mungkin maksudnya jawaban (3⁷ⁿ)⁵ + (3⁻⁷ⁿ)⁵ akan tersusun 3 angka a, b, dan c yang berulang.

• a < b < c
• a = 1
• b = 4
• c = 5
• c - a² - b² = 5 - 1² - 4² = 5 - 1 - 16 = 4 - 16 = - 12

Pelajari lebih lanjut

• Materi tentang Bilangan Berpangkat yomemimo.com/tugas/41920313

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