Question

porfis respondan :(( me falta esta pregunta, doy coronita :D

Answer 1

Respuesta:

32

Explicación paso a paso:

$\frac{a^{2}+b^{2} }{a^{2}- b^{2} } =\frac{85}{40} \\\\40\times (a^2+b^2)=85\times (a^2-b^2)\\\\40a^2+40b^2=85a^2-85b^2\\\\40b^2+85b^2=85a^2-40a^2\\\\125b^2=45a^2\\\\25b^2=9a^2\\\\Sacamos\ raiz\ cuadrada:\\\\5b=3a\\\\Reemplazamos\ en\ la\ otra\ ecuacion: \boxed {4a+5b=140}\\\\4a+3a=140\\\\7a=140\\\\a=\frac{140}{7} \\\\a=20\\\\Sabemos\ que:\boxed {5b=3a}\\\\5b=3\times20\\\\5b=60\\\\b=\frac{60}{5} \\\\b=12\\\\\\a+b=20+12=32$