The sum of the squares of two integers is 306 if the square of the larger interger is 25 times the smaller integer. Find the integers

let the larger integer be x and smaller be y

according to the question,

x2+ y2 = 306  ..........(1) 

x2 = 25y  ...........(2)

putting the value of x2 from (1) in (2), we get

so, 25y + y2= 306

  y2+25y- 306 = 0

y2 + 34y -9y - 306 = 0

y (y+34) -9 (y+34) =0

⇒(y+34) (y-9) = 0

y = -34  or  y = 9

 

WHEN y = -34 :

 

WHEN y =  9 :

 

So, larger integer = 15  and smaller integer = 9

 

 

 

 

 

  • 3

let the larger no. be x and smaller be y

according to the question,

x2+ y2 = 306 and x2 = 25y

so, 25y + y2= 306

y2+25y- 306= 0

y2 + 34y -9y - 306 = 0

y(y+34) -9 (y+34) =0

(y+34) (y-9) = 0

so y = -34 9

when y = -34

the larger no. = -√850

when y = 9

the larger no. = 15

  • 7

Thank you so much...:)

  • -1
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