What's in a reciprocal?

Algebra Level 3

True or False?

If x , y x, y are real numbers such that 1 x = 1 y , \frac{1}{x} = \frac{1}{y}, then

x = y x = y

Always true Always false Sometimes true, sometimes false

Chung Kevin by Chung Kevin , 45, Australia

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3 solutions

1 y = 1 x ⇒ 1 y − 1 x = 0 ⇒ x − y y x = 0 ⇒ x − y = 0 ⇒ x = y \quad \quad \quad \frac { 1 }{ y } =\frac { 1 }{ x } \\ \Rightarrow \quad \frac { 1 }{ y } -\frac { 1 }{ x } =0\\ \Rightarrow \quad \frac { x-y }{ yx } =0\\ \Rightarrow \quad x-y=0\\ \Rightarrow \quad x=y

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Jun Arro Estrella
Aug 22, 2015

Its obvious..hahaha 1/x=1/y, multiply xy on both sides we get x=y

0 Helpful 0 Interesting 0 Brilliant 0 Confused
Dev Sharma
Aug 21, 2015

1/x = 1/y

cross multiply,

y = x

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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