Question

If a= (√3+√2) / (√3-√2) and b= (√3-√2) / (√3+√2), find a^3+b^3
Please answer asap

Answer 1

$a = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3 } - \sqrt{2} } \\ b = \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ a + b = \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } + \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } \\ = \frac{( { \sqrt{3} + \sqrt{2} })^{2} + ( { \sqrt{3} - \sqrt{2} })^{2} }{3 - 2} \\ = 2(( { \sqrt{3} })^{2} + ( { \sqrt{2} })^{2} ) \\ = 2(3 + 2) \\ = 10 \\ ab = \frac{ \sqrt{3 } + \sqrt{2} }{ \sqrt{3} - \sqrt{2} } \times \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{3} + \sqrt{2} } = 1 \\ {a}^{3} + {b}^{3} = ( {a + b})^{3} - 3ab(a + b) \\ = ( {10})^{3} - 3.10 \\ = 1000 - 30 \\ = 970$

Answer 2

Answer:

a=

3

−

2

3

+

2

b=

3

+

2

3

−

2

a+b=

3

−

2

3

+

2

+

3

+

2

3

−

2

=

3−2

(

3

+

2

)

2

+(

3

−

2

)

2

=2((

3

)

2

+(

2

)

2

)

=2(3+2)

=10

ab=

3

−

2

3

+

2

×

3

+

2

3

−

2

=1

a

3

+b

3

=(a+b)

3

−3ab(a+b)

=(10)

3

−3.10

=1000−30

=970