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 , and , prove that

.

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. ðŸ™‚

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

yes. it’s too easy, but I am old ðŸ™‚

@puntomaupunto, these are for students only. ðŸ™‚

Pingback: Math Proof of the Week 1 Answer - Proofs from The Book