Question

If y=2+√3, Find the value of (a) y + 1/y (b) y2 + 1/y2 (c) y3 + 1/y3 (d) y4 + 1/y4

Answer 1

Answer:

y+

y

1

=9

Squaring both side

(y+

y

1

)

2

=9

2

y

2

+

y

2

1

+2×y×

y

1

=81

y

2

+

y

2

1

=81−2=79

Squaring

(y

2

+

y

2

1

)

2

=(79)

2

y

4

+

y

4

1

+2×y

2

×

y

2

1

=6241

y

4

+

y

4

1

=6,239.

Answer 2

Answer:

y+y/1=9

Squaring both side

(y+y1)2=92

y2+y21+2×y×y1=81

y2+y21=81−2=79

Squaring

(y2+y21)2=(79)2

y4+y41+2×y2×y21=6241

y4+y41=6,239.