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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.......