Solving a Quadratic Equation by Factorization Method
x ∧ 2+1 / x ∧...
Question
x^2+1/x^2=47 then x^2-1/x^2=?
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Solution
x²+1/x²=47 By completing the square, x²+1/x²+2*1/x*x=x²+1/x²+2=47+2 (x+1/x)²=49 x+1/x=√49=7 x²-1/x²=(x+1/x)(x-1/x) -----(1) (x-1/x)²=x²+1/x²-2=47-2=45 x-1/x=√45=3√5 From (1) x²-1/x²=7*3√5=21√5