Question

the number x is 2 more than the number y . If the sum of the squares of x and y is 34 ; find the product of x and y . Given x-y = 2 and x^2+ y^2= 34 , to find the value of xy.

Answer 1

Heya !!!

(X)² + (Y)² = 34 ------(1)

And,

X - Y = 2 ------(2)

From equation (2) we get,

X - Y = 2

X = 2+Y --------(3)

Putting the Value of X in equation (1)

(X)² + (Y)² = 34

(2+Y)² + (Y)² = 34

(2)² + (Y)² + 2 × 2 × Y + (Y)² = 34

4 + Y² + 4Y + Y² = 34

2Y² + 4Y -30 = 0

2Y² +10Y -6Y - 30 = 0

2Y(Y + 5) - 6 ( Y +5) = 0

( Y +5) ( 2Y -6) = 0

( Y +5) = 0 OR ( 2Y -6) = 0

Y = -5 OR Y = 3

Putting the Value of Y in equation (3)

X = 2 + Y

X = 2 + (-5) = -3

★Product of X and Y

X × Y = -3 × -5 = 15

HOPE IT WILL HELP YOU....... :-)

Answer 2

x - y = 2 

Square on both sides,


(x - y)² = 2²

x² + y² - 2xy = 4

 34 - 2xy      = 4

      -2xy       = 4 - 34
  
       -2xy      = -30
 
        2xy      = 30

          xy      = 30/2 

          xy      = 15 


Product of  x and y = 15


i hope this will help you

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