Answer:
y = -6.5 and x = 2
Step-by-step explanation:
Let one negative number be -y and another number be x
We are given that one negative number is 4.5 more than another number
So, -y=x+4.5
We are also given that The sum of the squares of these numbers is 46.25.
So,[tex]x^2+(-y)^2=46.25\\x^2+(x+4.5)^2=46.25\\x^2+x^2+20.25+18x=46.25\\2x^2+18x=26.25\\x^2+9x=13.125\\x^2+9x-13.125=0\\[/tex]
x=-6.5,2
When x = -6.5
-y=x+4.5
-y=-6.5+4.5
-y=-2
y=2
When x = 2
-y=x+4.5
-y=2+4.5
-y=6.5
y=-6.5
So, y = -6.5 and x = 2
