Question

If y=2+√3Find 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=2+√3

a) y+1/y

=(2+√3)+1/(2+√3)

={(2+√3)^2+1}/(2+√3)

=(4+3+2.2.√3+1)/(2+√3)

=(8+4√3)/(2+√3)

=4(2+√3)/(2+√3)

=4

b) y^2+1/y^2

=(y+1/y)^2-2.y.1/y

=4^2-2

=16-2

=14

c) y^3+1/y^3

=(y+1/y)^3-3.y.1/y(y+1/y)

=(4)^3-3.4

=64-12

=52

d) y^4+1/y^4

=(y^2+1/y^2)^2-2.y^2.1/y^2

=(14)^2-2

=196-2

=194