Question

If a =√5+√2/√5-√2
and b=√5-√2/√5+√2,
show that 3a² + 4ab – 3b² = 4 + 56/3√10​
​

Answer 1

Step-by-step explanation:

a+b= 14/3

a-b=4√10/3

ab=1

3a² + 4ab – 3b²

=3a² – 3b² +4ab

=3(a² – b²)+4ab

=3(a+b)(a-b)+4ab

=3(14/3)(4√10/3)+4×1

=4 + 56/3√10 (proved)