Question

Let $a\geq 1$ , and $A = \sqrt{1+\frac{1}{a}}$


1 - Show that $a(A+1)(A-1)=1$

2 - Show that $2\leq 1+A\leq 3$

Deduce that $1+\frac{1}{3a}\leq A\leq 1+\frac{1}{2a}$

Answer 1

Step-by-step explanation:

1) a(A+1)(A-1) = a(A^2 -1)

= a(1 + 1/a -1)

= a(1/a)

= 1