Question

The sum of two number is 4 and their products is 3 find and sum of their square and sum of their cubes

Answer 1

Answer:

10 and 28.

Step-by-step explanation:

Let the numbers are a and b.

  According to the question:  

     ⇒ ab = 3

     ⇒ a + b = 4

Square on both sides :

⇒ ( a + b )^2 = 4^2

⇒ a^2 + b^2 + 2ab = 4^2

⇒ a^2 + b^2 = 16 - 2ab

⇒ a^2 + b^2 = 16 - 2( 3 )          { ab = 3 }

⇒ sum of squares = 16 - 6

                              = 10

Cube on both sides:

⇒ ( a + b )^3 = 4^3

⇒ a^3 + b^3 + 3ab( a + b ) = 64

⇒ a^3 + b^3 + 3( 3 )( 4 ) = 64

⇒ a^3 + b^3 = 64 - 3( 3 )( 4 )

⇒ a^3 + b^3 = 64 - 36

⇒ sum of cubes = 28

Answer 2

hey there

the answer is in the attachment

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