Question

If x=3+2V2, find the value of x^2 + 1÷x^2

Answer 1

Answer:

Check the above attachment!✔️✔️✔️

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Answer 2

Answer:

(3210 - 8576 √2) / 357

Step-by-step explanation:

Given,

x = 3 +2√2

So,

x² = (3 + 2√2)²

= 9 + 12 √2 + 12√2

Using, (a +b)² = a² +2ab +b²

= 9 + 24 √2........(1)

Also,

1 / x² = 1 / (9+ 24 √2)

= 1 × (9- 24 √2)/ (81 - 1152)

Using, a² - b² = (a +b) (a -b)

= (9 -24 √2) / - 1071

= (24√2 - 9) / 1071

= 3 ( 8√2 -3) / 1071

= (8 √2 -3) / 357 ...........(2)

Now,. (1) + (2) gives,

(9 + 24 √2)+ (8 √2 -3) / 357

( 3213 + 8568 √2 + 8√2 - 3 ) / 357

(3210 - 8576 √2) / 357 Ans

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