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answer (i) :
by using identity (a+b)^2 = a^2+b^2+2ab.
(x+1/x)^2 =x^2 +1/x^2 +2 ×x ×1/x .
(11)^2 = x^2 + 1/x^2 +2.
121 = x^2 +1/x^2 +2.
121 - 2 = x^2 + 1/x^2 .
hence, x^2 +1/x^2 = 119...
answer (ii) :
again by using identity (a+b)^2 = a^2 +b^2 +2ab.
(x-1/x)^2 =x^2 +1/x^2 -2×x × 1/x.
(x-1/x)^2 = 66-2.
(x - 1/x )^2 = 64.
( x-1/x)^2 = 8^2.
square both side cancelled....
hence x-1/x = 8.
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