find value of a3-27b3 if a-3b=-6 and ab=-10?
回答 (3)
2016-05-30 8:30 am
a - 3b = -6 ...... [1]
(a - 3b)² = (-6)²
a² - 6ab + 9b² = 36
a² + 9b² = 6ab + 36
a² + 3ab + 9b² = 9ab + 36
But ab = -10, then :
a² + 3ab + 9b² = 9(-10) + 36
a² + 3ab + 9b² = -54 ...... [2]
a³ - 27b³ = a³ - (3b)³
a³ - 27b³ = (a - 3b)(a² + 3ab + 9b²) ...... [3]
Substitute [1] and [2] into [3] :
a³ - 27b³ = (-6) × (-54)
a³ - 27b³ = 324
(a - 3b)² = (-6)²
a² - 6ab + 9b² = 36
a² + 9b² = 6ab + 36
a² + 3ab + 9b² = 9ab + 36
But ab = -10, then :
a² + 3ab + 9b² = 9(-10) + 36
a² + 3ab + 9b² = -54 ...... [2]
a³ - 27b³ = a³ - (3b)³
a³ - 27b³ = (a - 3b)(a² + 3ab + 9b²) ...... [3]
Substitute [1] and [2] into [3] :
a³ - 27b³ = (-6) × (-54)
a³ - 27b³ = 324
2016-05-30 9:54 am
a^3 - 27b^3
= (3b - 6)^3 - 27b^3
= 27(b - 2)^3 - 27b^3
= -54(3b^2 - 6b + 4)
= -54[(a + 6)^2 - (a + 6) + 4]
= -54(a^2 + 11a + 34)
= -54(5a + 4)
if a - 3b = -6 and ab = -10
a - 3(-10/a) = -6
a + 30/a = -6
a^2 + 30 = -6a
a^2 + 6a + 30 = 0
(a + 3)^2 + 21 = 0
= (3b - 6)^3 - 27b^3
= 27(b - 2)^3 - 27b^3
= -54(3b^2 - 6b + 4)
= -54[(a + 6)^2 - (a + 6) + 4]
= -54(a^2 + 11a + 34)
= -54(5a + 4)
if a - 3b = -6 and ab = -10
a - 3(-10/a) = -6
a + 30/a = -6
a^2 + 30 = -6a
a^2 + 6a + 30 = 0
(a + 3)^2 + 21 = 0
2016-05-30 8:53 am
Find value of a³−27b³ if a−3b = −6 and ab = −10?
a³−27b³ = (a−3b) (a²+3ab+9b²)
a³−27b³ = (a−3b) (a²−6ab+9b²+9ab)
a³−27b³ = (a−3b) ((a−3b)²+9ab)
a³−27b³ = (−6) ((−6)²+9(−10))
a³−27b³ = (−6) (36−90)
a³−27b³ = (−6) (−54)
a³−27b³ = 324
a³−27b³ = (a−3b) (a²+3ab+9b²)
a³−27b³ = (a−3b) (a²−6ab+9b²+9ab)
a³−27b³ = (a−3b) ((a−3b)²+9ab)
a³−27b³ = (−6) ((−6)²+9(−10))
a³−27b³ = (−6) (36−90)
a³−27b³ = (−6) (−54)
a³−27b³ = 324
收錄日期: 2021-04-18 14:54:14
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