Question

there are two integers whose product is -36 and the difference 15 write the greatest integer out of those two integer?
18
9
12
-12​

Answer 1

Let first integer be x

and second integer be y

Given:-

Product of two integers = - 36

=> x × y = -36 ........( i ) eq

and difference is 15

x - y = 15 ..........( ii ) eq

By taking ( i ) eq

=> x = -36 /y ........( iii ) eq

Put the value of ( iii ) eq on ( ii ) eq

-36/y - y = 15

By taking lcm

-36 - y² = 15y

=> y² + 15y + 36 = 0

Split into middle term

=> y² +12y + 3y + 36 = 0

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

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

=> y = - 3 and y = - 12

when y = -3 then x is

x = -36/y

x = - 36 / - 3

x = 12

When y = - 12 then x is

x = -36/y

x = - 36 / -12

x = 3

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