Question

Find an integer knowing that the sum of its reciprocal is 65/8

Answer 1

Find an integer knowing that the sum of its reciprocal is 65/8

Hola!

$x= n\'umero\ entero\qquad\qquad\ \dfrac{1}{x}=n\'umero \ rec\'iproco$

$x+\dfrac{1}{x}=\dfrac{65}{8}\\\\\\\dfrac{x^2+1}{x}=\dfrac{65}{8}\\\\ 8(x^2+1)=65x\\\\8x^2+8-65x=0$

Aplicamos Baskhara

$8x^2-65x+8=0\\\\\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}\\\\\\\dfrac{65\pm\sqrt{65^2-4(8)(8)}}{2(8)}\to\dfrac{65\pm\sqrt{4225-256}}{16}\to\dfrac{65\pm\sqrt{3969}}{16}\to\dfrac{65\pm63}{16}\\\\\\\to\dfrac{65+63}{16}\to\dfrac{128}{16}= 8\\\\\\\to\dfrac{65-63}{16}\to\dfrac{2}{16}=\dfrac{1}{8}$

Número = 8       Recíproco= $\dfrac{1}{8}$

Espero que te sirva, salu2!!!!