If 3x-2y=11 and xy=12, find the value of 27x³-8y³.
Answers
Given : 3x – 2y = 11 and xy = 12
On Cubing 3x – 2y = 11 both sides, we get
(3x – 2y)³ = (11)³
(3x)³– (2y)³ – 3 ( 3x)( 2y) (3x – 2y) = 1331
[By Using an identity , (a - b)³ = a³ - b³ - 3ab(a - b)]
27x³– 8y³ – 18xy(3x - 2y) =1331
27x³– 8y³ – 18 x 12 x 11 = 1331
[3x – 2y = 11 and xy = 12]
27x³– 8y³ – 2376 = 1331
27x³– 8y³ = 1331 + 2376
27x³– 8y³ = 3707
Hence, the value of 27x³– 8y³ is 3707.
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Answer:
Step-by-step explanation:
On Cubing 3x – 2y = 11 both sides, we get
(3x – 2y)³ = (11)³
(3x)³– (2y)³ – 3 ( 3x)( 2y) (3x – 2y) = 1331
[By Using an identity , (a - b)³ = a³ - b³ - 3ab(a - b)]
27x³– 8y³ – 18xy(3x - 2y) =1331
27x³– 8y³ – 18 x 12 x 11 = 1331
[3x – 2y = 11 and xy = 12]
27x³– 8y³ – 2376 = 1331
27x³– 8y³ = 1331 + 2376
27x³– 8y³ = 3707