Question

Se tiene
$\frac{a}{b} + \frac{b}{a} = 2$
Calcula
$\frac{ {a}^{2} + {b}^{2} }{ {b}^{2} }$
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Answer 1

Solución en la imagen adjunta

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Answer 2

Respuesta:

2

Explicación paso a paso:

$\frac{a}{b} + \frac{b}{a} = 2$

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

${a}^{2} + {b}^{2} = 2ab$

${a}^{2} - 2ab + {b}^{2} = 0$

${(a - b)}^{2} = 0$

$a - b = \sqrt{0}$

$a - b = 0$

$a = b$

Calcula:

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