Question

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

Answer 1

Answer:

125x³ + 27y³ = 2656

Step-by-step explanation:

Given:

• 5x + 3y = 16
• xy = 2

To find: 125x³ + 27y³

Solution:

125x³ = (5x)³ & 27y³ = (3y)³

=> 125x³ + 27y³ = (5x)³ + (3y)³

${a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )$

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