Answer:
see explanation
Explanation:
(1)
f(x) = g(x) , that is
- x² + 3x - 2 = - x + 1 ( add x to both sides )
- x² + 4x - 2 = 1 ( subtract 1 from both sides )
- x² + 4x - 3 = 0 ( multiply through by - 1 )
x² - 4x + 3 = 0 ← in standard form
(x - 1)(x - 3) = 0 ← in factored form
equate each factor to zero and solve for x
x - 1 = 0 ⇒ x = 1
x - 3 = 0 ⇒ x = 3
(2)
let x and y be the 2 numbers : x > y , then
x + y = 217 → (1)
x - y = 85 → (2)
add the 2 equations term by term to eliminate y
2x + 0 = 302
2x = 302 ( divide both sides by 2 )
x = 151
substitute x = 151 into (1)
151 + y = 217 ( subtract 151 from both sides )
y = 66
the 2 numbers are 66, 151