Question

$A^2+B^2$ es DP a $A^2-B^2$. Si cuando $A^2+B^2$ = 10, $A^2-B^2$ = 8, ¿Cuál es el valor de A cuando B = 7?

Answer 1

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

$\frac{10}{8} = \frac{ {a}^{2} + {7}^{2} }{ {a}^{2} - {7}^{2} }$

$\frac{10}{8} = \frac{ {a}^{2} + 49 }{ {a}^{2} - 49 }$

$10( {a}^{2} - 49) = 8( {a}^{2} + 49)$

$10 {a}^{2} - 490 = 8 {a}^{2} + 392$

$10 {a}^{2} - 8 {a}^{2} = 392 + 490$

$2 {a}^{2} = 882$

${a}^{2} = \frac{882}{2}$

${a}^{2} = 441$

$a = \sqrt{441}$

$a = 21$