Question

2 Calcular :
Si : a2 + b2 = 22
a-b=2
Calcula : p = raiz ab

Answer 1

Explicación paso a paso:

${a}^{2} + {b}^{2} = 22 \\ a - b = 2 \\ a = 2 + b \\ {(2 + b)}^{2} + {b}^{2} = 22 \\ 4 + 4b + {b}^{2} + {b}^{2} = 22 \\ 2 {b}^{2} + 4b + 4 = 22 \\ 2 {b}^{2} + 4b + 4 - 22 = 0 \\ 2 {b}^{2} + 4b - 18 = 0 \\ {b}^{2} + 2b - 9 = 0 \\ ({b}^{2} + 2b + 1) = 0 + 9 + 1 \\ ( {b + 1)}^{2} = 10 \\ \sqrt{ {(b + 1)}^{2} } = \sqrt{10} \\ b + 1 = \sqrt{10} \\ b = \sqrt{10} - 1 \\ a = 2 + b \\ a = 2 + \sqrt{10} - 1 \\ a = 1 + \sqrt{10}$

$p = \sqrt{( \sqrt{10} + 1)( \sqrt{10} - 1)} \\ p = \sqrt{10 - 1} \\ p = \sqrt{9} \\ p = 3$