MHB Given a quadratic in x, find the cube of x

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To find \( x^3 \) given \( x^2 = x + 3 \), one can first rearrange the equation to form \( x^2 - x - 3 = 0 \) and apply the quadratic formula. Once the values of \( x \) are determined, \( x^3 \) can be calculated using the relationship \( x^3 = x \cdot x^2 \). Substituting \( x^2 \) from the original equation into this expression simplifies the calculation. The final result for \( x^3 \) can be derived directly from these steps.
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if $x^2 = x+3$ then $x^3 = ??$ Not sure about this would appreciate some help
 
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Assuming that your question is the following:

If $x^2=x+3$, then find $x^3$

Here, we need to find what $x$ is, and to do so, we can apply the quadratic formula on $x^2-x-3=0$
 
Rido12 said:
Assuming that your question is the following:

If $x^2=x+3$, then find $x^3$

Here, we need to find what $x$ is, and to do so, we can apply the quadratic formula on $x^2-x-3=0$

Thanks a lot have got it
 
Thread 'Erroneously finding discrepancy in transpose rule'

Thread 'Erroneously finding discrepancy in transpose rule'

Obviously, there is something elementary I am missing here. To form the transpose of a matrix, one exchanges rows and columns, so the transpose of a scalar, considered as (or isomorphic to) a one-entry matrix, should stay the same, including if the scalar is a complex number. On the other hand, in the isomorphism between the complex plane and the real plane, a complex number a+bi corresponds to a matrix in the real plane; taking the transpose we get which then corresponds to a-bi...
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