Question

if x is equal to 9 minus 4 root 5 then find of x square + 1 upon x square

Answer 1

Your question:- If x=9-4√5, then find x²+1/x².

Answer:

x²+1/x² is equal to 322

Step-by-step explanation:

x=9-4√5

Therefore,

1/x=1/(9-4√5)

Now we will rationalise the number,

1/x = 1/(9-4√5) × (9+4√5)/(9+4√5)

1/x = (9+4√5) / [ (9-4√5)(9+4√5) ]

Applying (a-b)(a+b) = a²-b² to the denominator,

1/x = (9+4√5)/(9²- 4²×√5²)

1/x = (9+4√5)/(81-80)

Hence, 1/x = 9+4√5

x² + 1/x² is the same as (x + 1/x)²- 2(x × 1/x)

Therefore,

x²+1/x² = [(9-4√5)+(9+4√5)]² - 2×1

x²+1/x² = 18²-2 = 324-2 = 322

The value of x²+1/x² is equal to 322

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