Did you not check with this?
https://www.jiskha.com/questions/1829690/let-f-x-3x2-2x-n-and-g-x-mx2-nx-2-the-functions-are-combined-to-form-the
Let f(x) = 3x^2 – 2x + n and g(x) = mx^2 – nx + 2. The functions are combined to form the new functions h(x) = f(x) - g(x) and j(x) = f(x) + g(x). Point (6, 2) is in the function h(x), while the point (-2, 10) is in the function j(x). Determine the exact values of m and n.
Could someone please show me the full solutions, I've tried so many times so I want to see where I went wrong.
2 answers
so why don't you show us your work?
h(x) = (3x^2 – 2x + n)-(mx^2 – nx + 2) = (3-m)x^2 + (-2+n)x + (n-2)
j(x) = (3x^2 – 2x + n)+(mx^2 – nx + 2) = (3+m)x^2 + (-2-n)x + (n+2)
You know that h(6) = 2 and j(-2) = 10, so plug them in and you have
(3-m)*36 + (-2+n)*6 + (n-2) = 2
(3+m)*4 + (2+n)*2 + (n+2) = 10
or, more usefully,
-36m+7n = -92
4m+3n = -8
solve these (multiply #2 by 9 and add to eliminate x) and you get
m = 55/34
n = -82/17
h(x) = (3x^2 – 2x + n)-(mx^2 – nx + 2) = (3-m)x^2 + (-2+n)x + (n-2)
j(x) = (3x^2 – 2x + n)+(mx^2 – nx + 2) = (3+m)x^2 + (-2-n)x + (n+2)
You know that h(6) = 2 and j(-2) = 10, so plug them in and you have
(3-m)*36 + (-2+n)*6 + (n-2) = 2
(3+m)*4 + (2+n)*2 + (n+2) = 10
or, more usefully,
-36m+7n = -92
4m+3n = -8
solve these (multiply #2 by 9 and add to eliminate x) and you get
m = 55/34
n = -82/17