a² +1/a² = 7, find the value of a²- 1/a²
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Step-by-step explanation:
a²+1/a²-2×a×1/a =7-2
(a-1/a)² = 5
(a-1/a) =+/- root 5 --- A
a²+1/a²+2a×1/a =7+2 =9
(a+1/a)² = 9
a+1/a = +/- 3 ------ B
A×B = (a+1/a)(a-1/a) = a²-1/a² = 3×root5 or -3×root5
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