Math, asked by jitenderChad413, 1 year ago

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.

Answers

Answered by Galaxy
162
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







Answered by VishalSharma01
205

Answer:

Step-by-step explanation:

Solution :-

Let the smaller number be x,

Then,

Square of the larger number = 18x

Square of the smaller number = x²

Sum of the squares of the integers = 208

According to the question,

⇒ x² + 18x = 208

x² + 18x - 208 = 0

By using prime factorization method, we get

x² + 26x - 8x - 208 = 0

⇒ x(x + 26) - 8(x + 26) = 0

⇒ (x + 26) (x - 8) = 0

⇒ x + 26 = 0 or x - 8 = 0

x = - 26, 8 (As x can't be negative)

x = 8

Square of larger number = 18x = 18 × 8 = 144

Larger number = √144 = 12

Hence, the number are 8 and 12.

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