if x-1/x =3 find x^2+1/x^2
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Given
x-1/x = 3---(1)
On Squaring equation (1), we get
=> (x-1/x)² = 3²
=> x²+1/x²-2*x*(1/x) = 9
/* By algebraic identity :
(a-b)² = a²+b²-2ab */
=> x²+1/x² - 2 = 9
=> x² + 1/x² = 9 +2
=> x² + 1/x² = 11
Therefore,
x²+1/x² = 11
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