Question

please give me the answers​

Answer 1

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)