# The sum of the squares of two positive integer is 208. if the square of the larger number is 18 times the smaller number find the numbers.

1

2015-05-09T12:43:35+05:30

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GIVEN ;-

⇒ Sum of Squares of two positive numbers are  = 208

⇒Sum of larger number is 18 times  the smaller number

TO FIND ;-

⇒ Find the two numbers = ?

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