Question

if 5x+3y=16 and xy=2, find the value of 125x3 + 27y3

Answer 1

Answer:

★Given:-

• 5x + 3y = 16
• xy = 2

★To find:-

• 125x³ + 27y³

★Solution:-

125x³ = (5x)³ & 27y³ = (3y)³

=> 125x³ + 27y³ = (5x)³ + (3y)³

a³+b³=(a+b)(a²-ab+b²)

Here, a = 5x & b = 3y

=> (5x)³ + (3y)³ = (5x + 3y) ( (5x)² - 5x*3y + (3y)² )

=> (5x)³ + (3y)³ = 16 ( (5x)² - 15xy + (3y)² )

Adding and subtracting 30xy, we get

=> (5x)³ + (3y)³ = 16 ( (5x)² - 15xy + (3y)² + 30xy - 30xy )

=> (5x)³ + (3y)³ = 16 ( (5x)² + 30xy + (3y)² - 15xy - 30xy )

=> (5x)³ + (3y)³ = 16 ( (5x)² + 30xy + (3y)² - 45xy )

=> (5x)³ + (3y)³ = 16 ( (5x+3y)² - 45xy )

=> (5x)³ + (3y)³ = 16 ( (16)² - 45(2) )

=> (5x)³ + (3y)³ = 16 ( 256 - 90 ) = 16 (166) =

2656

(Ans)

Answer 2

Answer:

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