Question

Q11 Write a pair of integers whose product is-36 and whose difference is 15

Answer 1

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Let the 2 integers be x and y respectively.

Given:
product = -36
difference = 15

xy = -36. ...[ i ]

x - y = 15
x = 15 + y. ...[ II ]

putting the value of x in eq. [ i ]

xy = -36

( 15 + y) y = -36

15y + y ^2 = -36

y^2 + 15y + 36 = 0

y^2 + 12y + 3y + 36 = 0

y ( y + 12 ) + 3 ( y + 12 ) = 0

(y + 3) (y + 12) = 0

y = -3, y = -12

y = -3
x = 15 + y
= 15 + (-3)
= 15 - 3
= 12

y = -12
x= 15 + ( -12)
x = 15 -12
x = 3


The two pair integers are -3 and 12 or 3 and - 12


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Answer 2

Answer:

Let the 2 integers be x and y respectively.

Given:

product = -36 difference = 15

xy = -36.

X - y = 15 x = 15 + y.

.[i]

.[ II ]

putting the value of x in eq. [i]

xy = -36

(15+ y) y = -36

15y + y^2 = -36

y^2 + 15y + 36 = 0

y^2 + 12y + 3y + 36 = 0

y(y + 12 ) + 3y 12 ) = 0

(y + 3) (y + 12) = 0

y=-3, y=-12

y=-3 x = 15+ y = 15 + (-3) = 15 - 3 = 12

y=-12 x= 15+ (-12) x = 15 -12 x=3

The two pair integers are -3 and 12 or 3 and - 12