Comparison of two values I have to figure out the relation between the quantity ( 0.9 <mr

Kazeljkaml5n9y

Kazeljkaml5n9y

Answered question

2022-04-10

Comparison of two values
I have to figure out the relation between the quantity ( 0.9 / 1.1 ) 2 + ( 1.1 / 0.9 ) 2 and 2. How can i do this without explicitly calculating the first value, by using some laws of exponents?

Answer & Explanation

Layne Bailey

Layne Bailey

Beginner2022-04-11Added 16 answers

I think the easiest way to see it is to use the following inequality: For x > 0, the following holds:
x + 1 x 2
with equality only if x = 1. This you can see by multiplying out by x and then you get the equivalent expression x 2 + 1 2 x = ( x 1 ) 2 0, which is true (and again equality only holds if x = 1).
In your case just plug in x = ( 0.9 1.1 ) 2 , which is > 0 and 1, to get x + 1 x > 2
revistasbibxjm87

revistasbibxjm87

Beginner2022-04-12Added 3 answers

The expression has the form x 2 + 1 x 2 . Now observe that,
x 2 + 1 x 2 2 x 2 2 + 1 x 2 = ( x 1 x ) 2 0.

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