+69 Find all solutions to:
ab + 2a + 2b = −16
ac + 2a + 2c = 26
bc + 2b + 2c = −14.
+15000 Find all solutions to:
ab + 2a + 2b = −16
ac + 2a + 2c = 26
bc + 2b + 2c = −14
Hello juananother!
\( ab + 2a + 2b = −16\\ a(b+2)+2b=-16\\ a= -\dfrac{16+2b}{b+2}\\ \ \\ ac + 2a + 2c = 26\\ a(c+2)+2c=26\\ a= \dfrac{26-2c}{c+2} \)
\( -\dfrac{16+2b}{b+2}=\dfrac{26-2{ \color{BrickRed} c}}{{ \color{BrickRed} c}+2} \)
\(bc + 2b + 2c = −14\\ \color{BrickRed} c=( -\dfrac{14+2b}{b+2}) \)
\(-\dfrac{16+2b}{b+2}= \dfrac{26-2{ \color{BrickRed} (-\dfrac{14+2b)}{b+2}}}{{ \color{BrickRed} (-\dfrac{14+2b}{b+2})}+2}\)
\(b= -\dfrac{8}{3}\)
\(c= -\dfrac{14+2\cdot (-\dfrac{8}{3})}{-\dfrac{8}{3}+2}\)
\(c=-13\)
\(a= \dfrac{26-2(-13)}{(-13)+2} \)
\(a=-\dfrac{52}{11}\)
!
There have been at least two other (with better methods than this one) answers to this question posted within the last week.
Look for them.
+15000 "with better methods than this one" Is there any better math than right? At school?
!
Some methods are certainly better than others.
(Both good and bad methods should lead to the correct answer.)
Have you looked at the earlier answers ?
