a^2+ab = 15

2b^2 = 20 - 2ab

what could a+b be worth?

1. 35

2. 25

3. -25

4. -5

Guest Oct 23, 2014

#1**+5 **

ok lets think about this

$$\\a^2+ab = 15 \qquad (1a)\\

a(a+b)=15 \qquad (1b)\\

a=\frac{15}{a+b} \qquad\qquad (1c)\\\\\\

2b^2 = 20 - 2ab\qquad (2a)\\

b^2=10-ab\qquad (2b)\\

b^2+ab=10\qquad (2c)\\

b(b+a)=10\qquad (2d)\\

b=\frac{10}{b+a}\qquad\qquad(2e)\\$$

So if

$$\\If\;\;a+b=35\;\;then\;\;a=15/35\;\;and\;\; b=10/35\\\\

If\;\;a+b=25\;\;then\;\;a=15/25\;\;and\;\; b=10/25\\\\

If\;\;a+b=-25\;\;then\;\;a=-15/25\;\;and\;\; b=-10/25\\\\

If\;\;a+b=-5\;\;then\;\;a=-15/5\;\;and\;\; b=-10/5\\\\

simplifying\;\; each \;\;of \;\;these\\\\\\

If\;\;a+b=35\;\;then\;\;a=3/7\;\;and\;\; b=2/7\\

BUT\qquad 3/7+2/7\ne35\;\; So\;\; no\;\; good\\\\

If\;\;a+b=25\;\;then\;\;a=3/5\;\;and\;\; b=2/5\\

BUT\qquad 3/5+2/5\ne25\;\; So\;\; no\;\; good\\\\

If\;\;a+b=-25\;\;then\;\;a=-3/5\;\;and\;\; b=-2/5\\

BUT\qquad -3/5+-2/5\ne-25\;\; So\;\; no\;\; good\\\\

If\;\;a+b=-5\;\;then\;\;a=-3\;\;and\;\; b=-2\\

AND\qquad -3+-2=-5\;\; So\;\; this\;\;answer\;\;is\;\; good\\\\$$

So a+b could be worth -5

Melody
Oct 24, 2014

#2**+5 **

a^2+ab = 15 → b = (15- a^2)/a

2b^2 = 20 - 2ab → b^2 = 10 - ab → [(15 - a^2)/a]^2 = 10 - (15 - a^2) →

(15 - a^2)^2 = a^2(a^2 - 5) →

225 - 30a^2 + a^4 = a^4 - 5a^2 →

-25a^2 + 225 = 0

25a^2 - 225 = 0

a^2 - 9 = 0

(a + 3) (a - 3) = 0

a = -3 a = 3

b = -2 b = 2

Then....... -3 + -2 = -5

CPhill
Oct 24, 2014

#3**+5 **

there you go.

2 good approaches - 2 good answers.

CPhill's is a little more 'mathematical' than mine but mine's more fun.

Melody
Oct 24, 2014

#5**0 **

Ok you got me Chris.

Now yours really is more fun.

Look what you have done now.

Did you know that greif tears have got more protein in them than 'onion' tears and one possible reason is that the protein acts like a sort of glue making the tears form perfect droplets and it also slows them rolling down the face. Hence the protein increases the visual stimuli of tears. People are hard wired to respond to tears. So cave people who cried when they were greiving or in pain were likely to be looked after better and were hence more likely to survive then those that could not produce the tears.

It is just a theory. But I like it. :)

How are my triple tears affecting you Chris.

Melody
Oct 24, 2014