Realtomcruise62
New member
- Joined
- Feb 5, 2023
- Messages
- 4
Problem is:
Two numbers differ by 6. If the numbers are square and then added, the sum if 146. Determine the numbers.
My working is:
Let x be the greater number and y the lesser
x - 6 = y
x^2 + y^2 = 146
using substitution:
x^2 + (x - 6)^2 = 146
Then expanding:
2x^2 - 12x + 36 = 146
2x^2 - 12x - 110 = 0
2(x^2 - 6x - 55) = 0
2(x - 11)(x + 5) = 0
Thus x is 11 and -5, but the difference between the two is 16, not 5
Where did I go wrong, thanks in advance
EDIT: I am a retard, here’s the piece I forgot about:
x = 11 or -5
x = 11
11 - 6 = y
y = 5
or
x = -5
-5 - 6 = y
y = -11
Therefore the two numbers are 11 and 5 OR -5 and -11
I assumed the roots of the quadratic were different variables for whatever reason, first time I’ve seen multiple solutions as part of a quadratic in a systems of equations problem. Mods leave this thread up for archival purposes, this seems to be nice site here and I may offer help in return at some point if I ever gain some more competence lmao, seems like a good bit of extra practice.
Two numbers differ by 6. If the numbers are square and then added, the sum if 146. Determine the numbers.
My working is:
Let x be the greater number and y the lesser
x - 6 = y
x^2 + y^2 = 146
using substitution:
x^2 + (x - 6)^2 = 146
Then expanding:
2x^2 - 12x + 36 = 146
2x^2 - 12x - 110 = 0
2(x^2 - 6x - 55) = 0
2(x - 11)(x + 5) = 0
Thus x is 11 and -5, but the difference between the two is 16, not 5
Where did I go wrong, thanks in advance
EDIT: I am a retard, here’s the piece I forgot about:
x = 11 or -5
x = 11
11 - 6 = y
y = 5
or
x = -5
-5 - 6 = y
y = -11
Therefore the two numbers are 11 and 5 OR -5 and -11
I assumed the roots of the quadratic were different variables for whatever reason, first time I’ve seen multiple solutions as part of a quadratic in a systems of equations problem. Mods leave this thread up for archival purposes, this seems to be nice site here and I may offer help in return at some point if I ever gain some more competence lmao, seems like a good bit of extra practice.
Last edited by a moderator: