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,

*x*^{2}+ *y*^{2} = 306 ..........(1)

*x*^{2} = 25*y* ...........(2)

putting the value of *x*^{2 }from (1) in (2), we get

so, 25*y* + *y*^{2}= 306

* y*^{2}+25*y*- 306^{ }= 0

⇒*y*^{2} + 34*y* -9*y *- 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

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