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Step-by-step explanation:
(I) x+1/x=4
now,
2x2+2/x2
=2(x2+1/x2)
= 2{(x+1/x)2-2x*1/x}
= 2(4^2 -2)
=2(16-2)
= 2*14
= 28
again
3x3+3/X3
= 3(X3+1/X3)
= 3{(x+1/x)^3-3x*1/x*(x+1/x)}
= 3(4^3-3*4)
= 3(64-12)
= 3*52
= 156
(ii) 2x-2/x=4
x-1/x = 2
now
x2+1/x2
= (x-1/x)2+2*x*1/x
= 2^2 +2
= 4+2
=6
again
X3+1/X3
= (x-1/x)3+3*x*1/x(x-1/x)
= 2^3 -3*2
= 8-6
=2
(iii)
given
x2+1/x2 = 62
(x+1/x)2 -2*x*1/x = 62
(x+1/x)2 -2 = 62
(x+1/x)2 = 62+2
(x+1/x)2 = 64 = 8^2
x+1/x = 8 (taking positive value only)