Easy but Hard!!!

Algebra Level 2

Set A is defined as

A={x: $√x$ > x-1, x $\in N$ }

Find n(A).

2 solutions

Cantdo Math
Apr 29, 2020

Since $\sqrt{x}-x+1$ is a decreasing function on $x \ge 1$ .So,after observing $x \ge 3$ doesn't work.It follows that only 1 and 2 are elements of A.

Aryan Sanghi
May 12, 2018

x can only be 1 or 2 as for values greater than two, √x>x-1 for natural x.

How do you know that any integer above 2 doesn't satisfy this criteria?

Pi Han Goh - 3 years ago

Good question sir.

As √3=1.732<2 √4=2<3

n-1 gets greater and greater than √n after n=2

Aryan Sanghi - 3 years ago