3
.1. Solve the equation : x°-15-126=0 by Cardan's Method.
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To Solve : For Values of x such that
Here,
Therefore, x must be a binomial.
Calculating the nature of roots:
Now,
Let x being a binomial.
Therefore, Simutaneously, we must conclude that
Now, Multiplying First Equation by (u)³ on both sides and substituting using second equation
But, As u and v are indistinguishable. And, u≠v
Therefore,
And, Thus,
Therefore, All the values of x are:
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