What is the solution of the equation x^3 - 7x + 6 = 0

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We have to solve the equation x^3 - 7x + 6 = 0

This can be solved using the formula to find the roots of a cubic equation but the process is a long drawn one.

Instead, let's assume this has integer roots and factorize it:

x^3 - 7x + 6 = 0

=> x^3 - x - 6x + 6 = 0

=> x(x^2 - 1) - 6(x - 1) = 0

=> x(x - 1)(x + 1) - 6(x - 1) = 0

=> (x - 1)[x^2 + x - 6] = 0

=> (x - 1)(x^2 + 3x - 2x - 6) = 0

=> (x - 1)(x(x + 3) - 2(x + 3)) = 0

=> (x - 1)(x - 2)(x + 3) = 0

=> x = 1, x = 2 and x = -3

The roots of the equation are x = 1, x = 2 and x = -3

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