jmc

Question

Positive real numbers r,s satisfy the equations r^2 + s^2 = 1 and r^4 + s^4= 78. Find rs.

Accepted Answer

We have 2r^2s^2 = (r^4 + 2r^2s^2 + s^4) - (r^4 + s^4) = (r^2 + s^2)^2 - (r^4 + s^4) = (1)^2 - 78 = 18, so r^2s^2 = 116. This means that rs = 14.