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... We can also assume that m and n are relatively prime (= they have no common divisors - if they do, just divide them out of both). This implies that (at least) one of the two is odd. Multiply both sides by n and square: 2n2 = m2. This implies that m2 is even, which, in turn, implies that m is even (t ...
... We can also assume that m and n are relatively prime (= they have no common divisors - if they do, just divide them out of both). This implies that (at least) one of the two is odd. Multiply both sides by n and square: 2n2 = m2. This implies that m2 is even, which, in turn, implies that m is even (t ...
THE CUBIC FORMULA
... a detailed discussion of the cubic formula. Precalculus texts of today rarely consider the subject. Why? Because the cubic formula, unlike the quadratic formula, frequently involves awkward cube roots of complex numbers. Besides, excellent numerical methods are available, such as Newton’s iterative ...
... a detailed discussion of the cubic formula. Precalculus texts of today rarely consider the subject. Why? Because the cubic formula, unlike the quadratic formula, frequently involves awkward cube roots of complex numbers. Besides, excellent numerical methods are available, such as Newton’s iterative ...
