Question

if x+1/x=6 find the values of x-1/x and x²and1/x²​

Answer 1

Answer:

34 and 4√2

Step-by-step explanation:

x+1/x=6

Squaring both sides

x²+1/x²+2×x×1/x=6²

x²+1/x²+2=36                                          [a²+b²+2ab=(a+b)²]

x²+1/x²=34

Subtract 2 from both sides

x²+1/x²-2=32

x²+1/x²-2×x×1/x=32          

(x-1/x)²=32                                            [a²+b²-2ab=(a-b)²]

x-1/x=4√2

Answer 2

Answer:

4√2, 3(7+4√3), 1/3(7+4√3)

Step-by-step explanation:

x+1/x=6......(1)

square....

x²+1/x²=34

then

(x-1/x)²=x²+1/x²-2

=34-2

=32

x-1/x= 4√2.......(2)

from elation (1) +(2)

2x=6+4√2

x=3+2√2

x²=17+12√2

1/x²=17-12√2