Review question

If $yz=a^2$, can we prove that $1/(a+y) + 1/(a+z) = 1/a$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource

Ref: R6806

Question

If $yz=a^2$ prove that $\frac{1}{a+y} + \frac{1}{a+z} = \frac{1}{a}.$

By using this result, or otherwise, find the numerical values of

1. $\dfrac{1}{1+x^k} + \dfrac{1}{1+x^{-k}}$;
2. $\dfrac{1}{7+\sqrt{62}-\sqrt{13}} + \dfrac{1}{7+\sqrt{62}+\sqrt{13}}$;
3. $\dfrac{2}{5(2+5\log_b c)} + \dfrac{1}{5+2\log_c b}$;