Question

If a^2+ frac1a^2 = 51, then the value of a3 – fraca1^3 is​

Answer 1

Answer:

Answer

a

3

−b

3

=(a−b)(a

2

+b

2

+ab)

So,

x

3

−

x

3

1

=(x−

x

1

)(x

2

+

x

2

1

+x×

x

1

)

=(x−

x

1

)(x

2

+

x

2

1

+1)

=(x−

x

1

)(51+1)

=52(x−

x

1

)

Now,

(x−

x

1

)

2

=x

2

+

x

2

1

−2x×

x

1

(x−

x

1

)

2

=51−2=49

x−

x

1

=

49

=7

Therefore,

x

3

−

x

3

1

=52(x−

x

1

)

=52×7

=364