if a^2+1/a^2=18 and a is not 0,find: a-1/a
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Answer:
a - 1/a = 4
Step-by-step explanation:
(ii) a² + 1/a² = 18
Subtract 2 on both sides
⇒ a² + 1/a² - 2 = 18 - 2
⇒ a² + 1/a² - 2 = 16
⇒ a² + 1²/a² - 2 = 16
⇒ (a)² + (1/a)² - 2(a)(1/a) = 16
[Because (x - y)² = x² + y² - 2xy above x = a, y = 1/a]
⇒ (a - 1/a)² = 16
⇒ a - 1/a = √16
⇒ a - 1/a = 4
Identities used :-
(x - y)² = x² + y² - 2xy
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