1. Sep 17, 2010

### kalupahana

1. The problem statement, all variables and given/known data

..........................49ac-12b2
(4α-3β)(3α-4β) =------------------------
....................................a2

Deduce that, If 12b2< 49ac< 49b2/2

then β lies between 3α/4 and 4α/3

2. Relevant equations

α+β = -b/a

αβ = c/a

3. The attempt at a solution

Last edited: Sep 17, 2010
2. Sep 17, 2010

### kalupahana

I don't know how to do this.

3. Sep 17, 2010

### Mentallic

Well, start by expanding the left hand side of that equality. Use the related equations you've given and remember the fact that $$(a+b)^2=a^2+b^2+2ab$$

4. Sep 17, 2010

### kalupahana

12α2-25αβ + 12β2

Using this i got that this in terms of a, b & c.

Next part of the question is this. How should i do it

5. Sep 18, 2010

### Mentallic

Right so looking at your a2 and b2 part, if $$(a+b)^2=a^2+b^2+2ab$$ then $$a^2+b^2=(a+b)^2-2ab$$

6. Sep 21, 2010

### kalupahana

12α2 + 12β2 = (12α+12β)2 - 313αβ

Last edited: Sep 21, 2010
7. Sep 22, 2010

### Mentallic

No not quite. If you expanded that you would get $$(12a)^2+(12b)^2=144a^2+144b^2$$

$$12a^2+12b^2=12(a^2+b^2)=12((a+b)^2-2ab)$$

Now go on from this.