Question

If x+y =12 and xy= 27, find the value of x3 + y3

Answer 1

Given :

x+y =12 and xy= 27

To Find :

The value of $x^{3} + y^{3}$

Solution :

  $(x + y)^{3}$      = $x^{3} + y^{3} + 3xy(x + y)$

or, 12³          = x³ + y³ + 3×27×12 (given xy = 27 and x+y = 12)

or,  x³ + y³   =  1728 - 972

∴    x³ + y³   = 756

∴ The value of x³ + y³ is 756.

Answer 2

The value of $\bf {x}^{3} + {y}^{3}$ is 756.

Given:

• $x + y = 12$
• $xy = 27$

To find: Find the value of ${x}^{3} + {y}^{3}$

Solution:

Identify used:

$\boxed{\bf{(x + y)}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y) }$

Step 1:

Take cube of x+y=12

$( {x + y)}^{3} = ( {12)}^{3}$

Apply identity

${x}^{3} + {y}^{3} + 3xy(x + y) = 1728$

Step 2:

Put the values of x+y and xy

${x}^{3} + {y}^{3} + 3(27)(12) = 1728$

or

${x}^{3} + {y}^{3} +972 = 1728$

or

${x}^{3} + {y}^{3} = 1728 - 972$

or

${x}^{3} + {y}^{3} = 756$

Thus,

Value of ${x}^{3} + {y}^{3}$ is 756.

Learn more:

1) If x + y = 1, then the value of x3 + y3 + 3xy is

(1) 1 (2) 0

(3) 2 (4) 3

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