Comparison of two valuesI 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?

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Comparison of two valuesI 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?

Layne Bailey · Accepted Answer

I think the easiest way to see it is to use the following inequality: For   x  &amp;gt;  0, the following holds:  x  +      1    x    ≥  2with 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   &amp;gt;  0 and   ≠  1, to get   x  +      1    x    &amp;gt;  2

revistasbibxjm87 · Accepted Answer

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.

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

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