Question

solve it if u can ;p :- let a and b be positive integers. show that √2 lies between a/b and (a+2b)÷(a+b)

Answer 1

heyy frnd!!

A correct formulation would be

Considering 0<a,0<b for {a,b}∈R

If

ab<√2 then √2<a+2ba+b

because

Making a=λb we have

λ<√2<λ+2λ+1=1+1λ+1

Here f(λ)=1+1λ+1 is a decreasing function for λ>0 and f(√2)=1+1√2+1=√2 so we conclude that

for 0<λ<√2⇒f(λ)>√2

i hope this helps u 

plzz mark as the brainliest 

source : phd textbooks :)