Question

if p+1/p=x+y and p-1/p= x-p then the true statement is - A) x+y=0 B) x=y C) xy=1​

Answer 1

Answer:

Step-by-step explanation:

Assume w.lo.g x>y. Then the statement becomes xp−yp≤(x−y)p. Since y>0, divide through out by yp. So we need to show (xy)p−1≤(xy−1)p whenever x>y>0 and 0<p<1. Let t=xy. So we need to show tp−1≤(t−1)p whenever t>1 and 0<p<1.

This is a calculus problem.

Let f(t)=(t−1)p−(tp−1) where 0<p<1.

Show that the function f(t) is increasing for t≥1 and when 0<p<1.

So f(t)≥f(1) and f(1)=0. So, we get the desired result.

EDIT: To show f(t) is increasing for t≥1 and when 0<p<1.

We need to show 0<f′(t)=p(t−1)p−1−ptp−1 and since p>0, all we need to show is that (t−1)p−1>tp−1, ∀t>1 and 0<p<1.

Since 0<p<1, we need to show t1−p>(t−1)1−p which is true since p<1 and t>t−1>0.

Answer 2

Step-by-step explanation:

please follow RD SHARMA OR S. CHAND