Question

Heya......


1) The sum of the squares of two positive integers is 208. If the square of the larger number is 18 times the smaller , find the numbers


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Answer 1

Please see the attachment

Answer 2

$\huge \mathtt \red{heya \: mate}$


$here \: is \: ur \: answer$


$\huge \bf{GIVEN \: ;-}$



⇒ Sum of Squares of two positive numbers are  
= 208


⇒Sum of larger number is 18 times  the smaller

number


$\huge \bf{TO \: FIND \: ;-}$


⇒ Find the two numbers = ?


$\huge \bf{SOL \: ;-}$


⇒ Let us take one of the number as x ,


⇒ Also the other number as y .
 

According to the  question , { ''  if the square of the larger number is 18 times the smaller number " }


So by this statement we can write as ,


   ⇒           x²  =  18 y
 

⇒ x²  +  y²  = 208 { because the sum of the squares of two positive integer is                                 }208.


⇒  x²  +  y²  = 208


⇒ Let us find the y 


⇒18  y  +  y²   =   208


⇒   y²   +  18  y  -   208   =  0


⇒   y²   +  26  y -  8y  -    208   =  0


⇒  y  (  y + 26 ) - 8 ( y + 26 )   =   0


⇒  (  y+ 26  )  (  y  -  8  )         = 0


But in the question it has been given that the integers are in the positive.


⇒  (  y  -  8  )         =  0   


⇒         y               = 8


We got the value of one integer , now let us find the value of the another integer.......
 


x²  +  y²  = 208


x²  +  ( 8 )²  =  208


x²  +  64      =208


         x²       =  208-64

     
   x²       =  144
        

         x        =√ 144
        

         x         = 12


So the two numbers are - 12 and 8


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