Find all solutions to:
ab + 2a + 2b = −16
ac + 2a + 2c = 26
bc + 2b + 2c = −44
+288 Use Simon's Favorite Factoring trick!
ab + 2a + 2b = -16 becomes a(b + 2) + 2b = - 16.
Adding 4 on each side gives us:
a(b + 2) + 2(b + 2) = -12, simplifying to (a + 2)(b + 2) = -12
Doing this factoring method for other equations gives us:
(a + 2)(b + 2) = -12
(a + 2)(c + 2) = 30
(b + 2)(c + 2) = -40.
Multiplying those equations and square rooting gives us:
(a + 2)(b + 2)(c + 2) = 120
Applying thiss gives us
120/(c + 2) = - 12
120/(b + 2) = 30
120/(a + 2) = - 40
Can you solve for a, b, c from here?
