Solve in R the system { ((x+y=z)),(((1/x)+(1/y)=(1/z))) :}


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Question Number 177763 by lapache last updated on 08/Oct/22

$S o l v e i n R t h e s y s t e m$ ${\begin{cases} x + y = z \\ \frac{1}{x} + \frac{1}{y} = \frac{1}{z} \end{cases}$
Commented by mr W last updated on 08/Oct/22

$n o s o l u t i o n f o r x, y, z \in R .$ $x, y a r e r o o t s o f t^{2} - z t + z^{2} = 0, b u t t h i s$ $h a s n o r e a l r o o t s, b e c a u s e$ $t^{2} - z t + z^{2} = {(t - \frac{z}{2})}^{2} + \frac{3 z^{2}}{4} \neq 0 f o r z \neq 0 .$
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