If (a/b) + (b/a) = 2, then find (a/b) 10 - (b/a) 10 - Maths - Factorisation

Question

If (a/b) + (b/a) = 2, then find (a/b) 10 -
(b/a) 10

Vijay Kumar Gupta · Accepted Answer

It is given that,       ab+ba=2       
1Squaring both sides,               ab+ba2=22   ab2+ba2+2=4          ab2+ba2=2       
2Cubing both sides of  1                                                      ab+ba3=23      ab3+ ba3+3abbaab+ba=8                                    ab3+ ba3+32=8                                         ab3+ ba3+6=8                                                ab3+ ba3=2      
3Multiply 2   and 3   to get,     ab2+ba2   ab3+ ba3=2×2                     ab5+ba+ab+ba5=4                     ab5+ba5+ab+ba=4                                 ab5+ba5+2=4                                        ab5+ba5=2         
4Again square both sdies of 4   to get,            ab10+ba10=2This further implies that,       ab5-ba52=ab10+ba10-2                                      =2-2                                      =0This gives,      ab10-ba10 = ab52-ba52                                   =ab5+ba5   ab5-ba5                                   =2×0                                   =0

If (a/b) + (b/a) = 2, then find (a/b) 10 - (b/a) 10 .

If (a/b) + (b/a) = 2, then find (a/b) ¹⁰ - (b/a) ¹⁰ .