Respuesta :
The value of m + n is 12 where , m is 4 and n is 8
Vieta’s formulas are formulas that relate the coefficients of a polynomial to sums and products of its roots. It was discovered by Francois Vieta. The simplest application of Vieta’s formula is quadratics and are used specifically in algebra.
Rearranging the log
[tex]\frac{8}{\log n \log m}(\log x)^2 - \left(\frac{7}{\log n}+\frac{6}{\log m}\right)\log x - 2013 = 0[/tex]
Using the Vieta's Theorem,
The sum of the possible values of log x is [tex]\frac{\frac{7}{\log n}+\frac{6}{\log m}}{\frac{8}{\log n \log m}} = \frac{7\log m + 6 \log n}{8} = \log \sqrt[8]{m^7n^6}[/tex]
But the sum of the possible values of log x is the logarithm of the product of the possible values of x. Thus the product of the possible values of x is equal to [tex]\sqrt[8]{m^7n^6}[/tex]
It remains to minimize the integer value of [tex]\sqrt[8]{m^7n^6}[/tex].
Since m, n>1 , we can check that m = 2² and n = 2³.
Hence , m = 4 and n = 8
m + n = 4 + 8
=> 12
To know more about the Vieta's Theorem here
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