Question

Mean proportional of x and y is 15 and x+y=34 then (x, y)?

Answer 1

Answer:

( x , y ) = ( 25 , 9 ) or ( 9 , 25 )

Step-by-step explanation:

Given,

        Mean proportional of x and y is 15. It means x / 15 = 15 / y.

      ⇒ 15^2 = xy   ⇒ 225 = xy     ...( 1 )

Also,  

     x + y = 34

   ⇒ x = ( 34 - y )

Substituting the value of x in ( 1 ) :

⇒ ( 34 - y )y = 225

⇒ 34y - y^2 = 225

⇒ y^2- 34y = - 225

⇒ y^2 - 34y + 225 = 0

⇒ y^2 - ( 25 + 9 )y + 225 = 0

⇒ y^2 - 25y - 9y + 225 = 0

⇒ y( y - 25 ) - 9( y - 25 ) = 0

⇒ ( y - 25 )( y - 9 ) = 0

⇒ y = 25 or  y = 9.

     Thus,

       x = 34 - y

          = 34 - 9 or 25

          = 25 or 9

Thus, ( x , y ) = ( 25 , 9 ) or ( 9 , 25 ).