Question

5. The number x is 2 more than the number 1
the sum of the squares of x and y is 34: fim
the product of x and y.​

Answer 1

Answer:

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Step-by-step explanation:

Given,

x

2

+y

2

=34...(1)

x−y=2...(2) Squaring on both sides, we get

(x−y)

2

=2

2

⇒x

2

+y

2

−2xy=4

From equation (1), we have

34−2xy=4

⇒2xy=30

⇒xy=15

Answer 2

Answer:

Step-by-step explanation:

given

    x = y + 2

      x² + y² = 34

    x - y = 2

  squaring,  (x - y)² = 2²

            x² + y² - 2 x y = 4

            34 - 2 x y = 4

              x y = 15

===========================

 2x - 3y = 10          x y  = 16

 8x³ - 27 y³ = (2x - 3y) ( 4x² + 6 xy + 9 y²)

              = (2 x - 3y) [ (2x -3y)² + 18 xy ]

              = 10 * [ 10² + 18 * 16 ]

====================================

 x > 0  and  x² + 1/9x²  = 25 / 36

     (x + 1/3x)²  = x² + 1/9x² + 2/3  = 25/36  + 2/3

            (x + 1/3x)² = 49/36

                x + 1/3x = 7/6      , we drop the negative value as x > 0.

  x³ +  1/27x³  = (x +  1/3x) ( x² + 1/9x² - x/3x)

                    = 7/6 * (25/36 - 1/3)

                    = 7/6 * 1/36

                     = 7/216