Question

if x=a+1/a and y=a-1/a find the value of x^4-2x^2y^2+y^4​

Answer 1

Answer:

x+y=2ax-y=2/a(x+y)(x-y)=4x^2 - y^2=4Squareing both sides we getx^4+y^4-2x^2 y^2 =16

Answer 2

Answer:

Given, x=

a

+

a

1

;y=

a

−

a

1

so, x

2

=a+

a

1

+2;y

2

=a+

a

1

−2

Ans, x

2

−y

2

=a+

a

1

+2−a−

a

1

+2=4

Now, (x

2

−y

2

)

2

=(4)

2

=16...(1)

Also, (x

2

−y

2

)=x

4

−y

4

−2x

2

y

2

...(2)

From (1) & (2), x

4

+y

4

−2x

2

y

2

=16