3. If x = 3+2√2, find the value of x2 + 1/x2
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Answer:
x=3+2√2
then
x²=(3+2√2)²
= 9+8+12√2
= 17+12√2. ..... ....................(i)
now, 1/x² = 1/17+12√2
On rationalising
=17- 12√2/( 17)²-(12√2)²
= 17-12√2 / 289-288
= 17-12√2/ 1
= 17-12√2
So, x²+1/x²= (17+12√2) + (17-12√2)
=17+12√2+17-12√2
=17+17
=34
So your answer is 34
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