CPhill

You can put this one straight into the on-site calculator....

Here's the proof of this using the "Squeeze Theorem".....it's somewhat complicated, but if you have some patience, I think you will appreciate the geometry involved. The proof is the first one on the page.

y = 1/3x − 2

−2x + 6y = 18

Let's get the second line in the same form as the first one. So we have..

6y = 2x + 18     .....divide through by 6

y = 1/3x + 3

These lines have the same slope (1/3) but different y intercepts. Thus, they are parallel.

Tha answer is -8....multiplying the first two terms gives us 2....there is no middle term....and multiplying the last terms gives us -10.

And......... 2 - 10  = -8

Thanks, Aziz.....I needed to put the "a" in there to indicate "multiples" or "family"

Use the inverse tanget to calculate this...

tan^-1(4) = x ≈ 76°

Note that this could also be a 76° angle in the 3rd quadrant - ≈ 256° -  since the tangent is also positive there.

tan 60 = √3...so we have

√3 = 7/x     so...multiplying both sides by x and dividing by √3, we have

x = 7/√3 or   (7√3) / 3

(3√2 +√5) * (3√2 - √5) =

(√18 + √5) * ( √18 - √5) =

18 - 5 =

13

So we have......

[x - (3√5 + 2)] * [x + (3√5 - 2)] = 0

x^2 - (3√5 + 2)x + (3√5 - 2)x - [ 45 - 4] = 0

x^2 - 4x - 41 = 0

I'm not exactly sure what you mean by "family,' but any multiples of this function would produce the same roots.

Anyone else have other approaches/ideas ???

Am I missing something???

 219/36 = 73/12 ≈ 6.08333