Answer:
The two numbers are -5 and -4
Step-by-step explanation:
Assume that the first number is x and that the second number is x+1.
We know that the sum of their squares is 41. This means that:
x² + (x+1)² = 41
We will expand the brackets and factorize to get the value of x as follows:
x² + (x+1)² = 41
x² + x² + 2x + 1 = 41
2x² + 2x + 1 - 41 = 0
2x² + 2x - 40 = 0
We can divide all terms by 2 to simplify the equation:
x² + x - 20 = 0 ..........> equation required in part II
Now, we can factorize this equation to get the values of x:
x² + x - 20 = 0
(x-4)(x+5) = 0
either x = 4 .........> rejected because we know that x should be negative
or x = -5 ...........> accepted
Based on the above calculations, the two numbers are -5 and -4
Hope this helps :)