Q. 1165.0( 4 Votes )

Write a pair of i

Answer :

Let the integers be x and y, where x > y.

According to the question,


Product of integers = -36


x × y = -36


xy = -36 …(i)


Also, difference of integers = 15


x – y = 15 …(ii)


From equation (i),


xy = -36


…(iii)


Substituting equation (iii) into equation (ii), we get




x2 + 36 = 15x


x2 – 15x + 36 = 0


x2 – 12x – 3x + 36 = 0


x(x – 12) – 3(x – 12) = 0


(x – 3)(x – 12) = 0


x = 3 or x = 12


If x = 3,


Put x = 3 in equation (ii),


x – y = 15


3 – y = 15


y = 3 – 15


y = -12


One of the pair is (3, -12).


If x = 12,


Put x = 12 in equation (i),


x – y = 15


12 – y = 15


y = 12 – 15


y = -3


One of the pair is (12, -3).


Thus, two solutions are (3, -12) and (12, -3).


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