Question

Find 27a^3+64b^3, if 3a+4b=10 and ab=2

Answer 1

Step-by-step explanation:

Given: 27a³ + 64b³

3a + 4b = 10

ab = 2

squaring both side

(3a + 4b)² = (10)²

(3a)² + (4b)² + 2(3a)(4b) = 100

9a² + 16b² +24ab = 100

9a² + 16b² + 24(2) = 100 (ab = 2)

9a² + 16b² + 48 = 100

9a² + 16b² = 100 - 48

9a² + 16b² = 52

27a³ + 64b³ = (3a)³ + (4b)³

a³ + b³ = (a+b) (a² -ab + b²)

(3a + 4b)[(3a)² - 2 + (4b)²]

10(9a² - 2 +16b²)

10(52 - 2)

10(50)

500

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