a=1/a-5, find (i)a-1/a (ii)a+1/a (iii)a2-1/a2
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Step-by-step explanation:
a= 1/a-5
=> 1/a = a+5. ........(1)
=> 1 = a²+5a
=> a²+5a-1 = 0
=> a = -5/2±√ (25+4) / 2
a = -5/2±√29/2
putting the value of a gives answers
(ii) a+1/a = a+(a+5) = 2a+5
= -5±√29/2 +5
= ±√29/2
(i) a-1/a = a-(a+5)
= -5
(III) a²-1/a²= (a+1/a)(a-1/a)
= (-5/2)√29
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