if a²+1/a²=18 find (a-1/a) and (a+1/a)
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Answered by
3
a = 1/root 17
(a-1/a) =1-root 17
(a+1/a) =1+root 17
(a-1/a) =1-root 17
(a+1/a) =1+root 17
Answered by
4
a^2+1/a^2
= (a+1/a)^2 -2(a)(1/a)
now (a+1/a)^2 -2 = 18
(a+1/a)^2 =18+2 = 20
(a+1/a) = √20 = 2√5
and also a^2+1/a^2 = (a-1/a)^2 +2(a)(1/a) = 18
(a-1/a)^2 +2 = 18
(a-1/a)^2 = 18-2 = 16
(a-1/a) = √16 = 4
hence (a-1/a) =4 , (a+1/a) = 2√5
= (a+1/a)^2 -2(a)(1/a)
now (a+1/a)^2 -2 = 18
(a+1/a)^2 =18+2 = 20
(a+1/a) = √20 = 2√5
and also a^2+1/a^2 = (a-1/a)^2 +2(a)(1/a) = 18
(a-1/a)^2 +2 = 18
(a-1/a)^2 = 18-2 = 16
(a-1/a) = √16 = 4
hence (a-1/a) =4 , (a+1/a) = 2√5
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