If x = (2 - √5), then x² + 1/x² = ......
Answers
Answer:
18
Step-by-step explanation:
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Given :
x = √5 - 2
To find :
x² + 1 / x²
Solution :
x = √5 - 2
⇒ 1 / x = 1 / √5 - 2
⇒ 1 / x = 1 / √5 - 2 × √5 + 2 / √5 + 2
⇒ 1 / x = √5 + 2 / ( √5 )² - ( 2 ) ²
⇒ 1 / x = √5 + 2 / 5 - 4
⇒ 1 / x = √5 + 2
Now,
x + 1 / x = √5 + 2 + √5 - 2
x + 1 / x = 2 √5
Again,
On squaring both sides, we have ;
( x + 1 / x )² = ( 2 √5 ) ²
⇒ x² + 1 / x² + 2 = 20
⇒ x² + 1 / x² = 20 - 2
⇒ x² + 1 / x² = 18
Hence,
The value of x² + 1 / x² = 18.
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Answer:
x²+1/x²=-2
Step-by-step explanation:
x=2-√5
we know that [x+1/x]²=x²+1/x²+2*x*1/x
[x+1/x]²-2=x²+1/x²
here value of x is 2-√5 and 1/x is 1/2-√5
by rationalizing the denominator we get 1/x as -2+√5
now putting the values
2-√5-2+√5-2=x²+1/x²
-2=x²+1/x²
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