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A={x `in` R/2^x+3^x-13*6^x=0} what is sum of x^2? x `in` A

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ruals | (Level 1) Salutatorian

Posted July 23, 2013 at 5:37 PM via web

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A={x `in` R/2^x+3^x-13*6^x=0}

what is sum of x^2?

x `in` A

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aruv | High School Teacher | (Level 2) Valedictorian

Posted July 23, 2013 at 6:17 PM (Answer #2)

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Define a function

`f(x)=2^x+3^x-13 xx 6^x`

The zero of the function f(x) s the root of the equation

`2^x+3^x-13xx6^x=0`

``Observe from above graph x=-2 is zero of f(x)

Thus

`2^(-2)+3^(-2)-13xx6^(-2)=(1/4)+(1/9)-13/6^2`

`=(9+4)/36-13/36=0`  

Thus `x^2=(-2)^2=4`  and `-2inR and -2inA` .

Thus Ans=4

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