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### This Is a Certified Answer

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The key thing is to use the identity

In light of that, start by working the value of :

Add them and get

Use the earlier identity to find the value of :

Plug these values in the given expression and simplify :

In light of that, start by working the value of :

Add them and get

Use the earlier identity to find the value of :

Plug these values in the given expression and simplify :

### This Is a Certified Answer

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=

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

x=5-√24

1/x=1/5-√24

on rationalize

1/x=

__1__×__5+√24__=__5+√24__=5+√245-√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