1.

The product of two numbers x6 - y6 if one of the numbers is x-y then find the other number

Answer»

Given: the product of two numbers X^6 - y^6.

To FIND: if one of the numbers is x-y then find the other number

Solution:

  • Now we have given that the one of the numbers is x-y .
  • Let the other number be Z.

                    (x³)² - (y³)²

  • Now according to the formula a² - b² = (a-b)(a+b), we get:

                    ( x³ - y³)(x³ + y³)

  • Now according to the formula a³ - b³ = (a-b)(a²+ab+b²), we get:

                    (x - y)(x² + XY + y²)(x³ + y³)

  • Now according to the question, we have:

                    z × (x - y) = (x - y)(x² + xy + y²)(x³ + y³)

                    z = (x² + xy + y²)(x³ + y³)

Answer:

          So the other number is (x² + xy + y²)(x³ + y³).


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