Question

[tex]\sf\:Diketahui[/tex]
5-a⁻¹ = b⁻¹
5+a⁻² = b⁻²

Tentukan nilai dari
a ÷ b = .......
Dalam pecahan campuran

Answer 1

Jawaban nya adalah 3:2 atau 1 1/2

Answer 2

Penjelasan dengan langkah-langkah:

5 – a-¹ = b-¹

5 – 1/a = 1/b

1/a + 1/b = 5

a + b = 5

ab

a + b = 5ab ..... ♠

5 + a-² = b-²

5 + 1/a² = 1/b²

1/b² – 1/a² = 5

a² – b² = 5

(ab)²

a² – b² = 5(ab)² .... ♣

Penyelesaian

a² – b² = 5(ab)²

a + b 5ab

(a – b)(a + b) = (5ab)(ab)

(a + b)

a – b = ab ..... ♪

♠ a + b = 5ab

♪ a – b = ab –

2b = 4ab

2b = (2a)(2b) ..... ♥

→ 2a = 2b

2b

→ 2a = 1

→ a = ½

♪ a – b = ab

½ – b = ½b

½b + b = ½

3b = ½

2

3b = ½ × 2

3b = 1

b = ⅓

Jawaban pertanyaan :

a ÷ b = ½ ÷ ⅓

a ÷ b = ½ × 3/1

a ÷ b = 3/2

a ÷ b = 1½ ✔