Question

Si: a/b+b/a=3; determine el valor de: M =√((a^2+ab+b^2)/ab)

Answer 1

Explicación paso a paso:

$\frac{a}{b} + \frac{b}{a} = 3 \\ \frac{ {a}^{2} + {b}^{2} }{ab} = 3 \\ {a}^{2} + {b}^{2} = 3ab$

$m = \sqrt{ \frac{( {a}^{2} + ab + {b}^{2}) }{ab} } \\ m = \sqrt{ \frac{3ab + ab}{ab} } \\ m = \sqrt{ \frac{4ab}{ab} } \\ m = \sqrt{4} \\ m = 2$