Math Proof Problem of the Week 1

It’s Friday and as I have mentioned in the previous post, I will be posting proof problems that are accessible to advanced high school students every Friday. Here is the Mathematics Proof Problem of the Week.

If $a > b > 0$, and $a^2 + b^2 = 6ab$, prove that

$\displaystyle\frac{a + b}{a - b} = \sqrt{2}$.

The proof of this problem and the second Math Proof of the Week will be posted next Friday.

Again, the problems in this series are intended for advanced high school math students. If the proof is too easy for you, no need to answer it. 🙂

4 thoughts on “Math Proof Problem of the Week 1”

1. a^2 + b^2 = 6ab
by using completing the squares
a^2 + 2ab + b^2 = 6ab+ 2ab
(a+b)^2 = 8ab
a+b = +- 2sqrt(2ab)
a^2 – 2ab + b^2 = 6ab- 2ab
(a-b)^2 = 4ab
(a-b) = +- 2sqrt(ab)
(a+b)/(a-b) = sqrt2
2sqrt(2ab)/2(sqrtab) = sqrt2
sqrt2 = sqrt2

2. yes. it’s too easy, but I am old 🙂