Question

x^3+1/a^3=(a+1/a)^3-3(a+1/a)if a+1/a is given​

Answer 1

Answer:

using (a + b)^3 = a^3 + b^3 + 3ab(a + b)

a^3 + b^3 = (a + b)^3 - 3ab(a + b)

Now substituting the values from question:

a^3+(1/a)^3= (a+1/a)^3-3*a*1/a(a+1/a)

=^3-3*

=3-3

=0

Answer: A

Answer 2

$\bold\red{\frac{ \sqrt{3} - 1}{ \sqrt{3} + 1} = a + b \sqrt{3} }$

$\bold\green{\frac{( \sqrt{3} - 1) ( \sqrt{3} - 1 }{ \sqrt{3} + 1 \sqrt{3} - 1 } = a + b \sqrt{3} }$

$\bold\pink{\frac{3 + 1 -2 \sqrt{3} }{2} = a + b \sqrt{3} }$

$\bold\blue{2 - \sqrt{3} = a + b \sqrt{3}}$

$\bold\purple{a = 2 ~~~b = - 1}$