Question

The sum of two numbers is 1 and their product is-30 . what are the numbers?

Answer 1

There are 2 methods to do this sum.
==========================================================
1:Trial and error method.
By this method , we find that the numbers are -5 and +6.
Since the product is -ve and the sum is +ve the numbers must be 1 negative and the other positive respectively such that the +ve number's absolute value is greater than the -ve number's.Such numbers are -5 and +6.
===========================================================
2. Algebraic method.
Let the 2 numbers be x and y.
Therefore , x+y=1 and xy=-30
since x+y=1,y=1-x , right?.
Therefore, xy can be written as
x(1-x).
Given x(1-x)=-30
or,x-x²=-30
or,x²-x-30=0
or,x²+5x-6x-30=0
or,x(x+5)-6(x+5)
or,(x-6)(x+5)=0
either x-6=0 or x+5=0
either x=6 or x=-5
Since for the value of x the value of y will also change,
The numbers are -5 and +6.
Ans:The numbers are -5 and +6.