Just elegancy required

Algebra Level 3

$x=\dfrac{4}{(5^{1/2}+1)(5^{1/4}+1)(5^{1/8}+1)(5^{1/16}+1)}$

Find $(x+1)^{48}$ .

1 solution

Tanishq Varshney
Jan 7, 2016

Divide and multiply by $5^{\frac{1}{16}}-1$

Use $(a-b)(a+b)=a^2-b^2$ repetitively in the denominator

This simplifies to

$\large{\frac{4(5^{\frac{1}{16}}-1)}{4}}$

Thus $\large{(5^{\frac{1}{16}}-1+1)^{48}=5^3=125}$

Brilliant! I was going to do a binomial expansion... But that's why I can't write a solution :(

Jason Simmons - 5 years, 5 months ago