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2015-04-25T12:35:41+05:30

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The key thing is to use the identity
x^2+\frac{1}{x^2}=\left(x+\frac{1}{x}\right)^2-2

In light of that, start by working the value of x+\frac{1}{x}
x=5-\sqrt{24}
\frac{1}{x}=\frac{1}{5-\sqrt{24}}=\frac{1}{5-\sqrt{24}}\times\frac{5+\sqrt{24}}{5+\sqrt{24}}=\frac{5+\sqrt{24}}{5^2-\sqrt{24}^2}=\frac{5+\sqrt{24}}{25-24}=5+\sqrt{24}

Add them and get
x+\frac{1}{x}=5-\sqrt{24}+5+\sqrt{24}=10

Use the earlier identity to find the value of x^2+\frac{1}{x^2} :
x^2+\frac{1}{x^2}=\left(x+\frac{1}{x}\right)^2-2=10^2-2=98

Plug these values in the given expression and simplify :
10\left(x^2+\frac{1}{x^2}\right)-97\left(x+\frac{1}{x}\right)-10\\=10\left(98\right)-97\left(10\right)-10\\=\boxed{0}
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you are superb
haha ty :) i hope the steps are clear enough this time... just ask if something doesn't make sense... had to skip couple steps to make the solution not too lengthy..
what is your name rational
2015-04-25T12:41:21+05:30

This Is a Certified Answer

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Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.
If
x=5-√24
1/x=1/5-√24
on rationalize
1/x=1        × 5+√24    =5+√24  =5+√24
     5-√24      5+√24    25-25

on looking identity (x+1/x)²=x²+1/x²+2
x²+1/x²=(x+1/x)²-2
on putting value
(5-√24 +5+√24)² -2
100-2=98
According to question
10{x²+1/x²} -97{x+1/x)-10
10(98) -97(10)-10
980-970-10⇒980-980=0
Answer is o

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