Math Queston #6

Algebra Level 2

If a b = a + b b 1 a \otimes b = \frac{a+b}{b-1} , find the value of 10 11 10 \otimes 11 .

1.2 20.1 2.1 2.01

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2 solutions

Ethan Mandelez
Mar 30, 2021

This to most people, is a completely new mathematical statement! However, the same rules apply:

10 11 = 10 + 11 11 1 = 2.1 10⊗11 = \dfrac {10+11} {11-1} = 2.1

Below is also a graph f ( x , y ) = x + y y 1 f(x,y) = \dfrac {x+y} {y-1} , which shows the possible values of x , y x,y and the corresponding value of x y x⊗y . Unsurprisingly, the point A = ( 10 , 11 , 2.1 ) A = (10,11,2.1) is a point on the graph!

GeoGebra - 3D Calculator

Avner Lim
Mar 25, 2021

10 11 = 10 + 11 11 1 = 21 10 = 2.1 10 \otimes 11 = \frac{10+11}{11-1} = \frac{21}{10} = \boxed{2.1}

Nice problem :D

Ethan Mandelez - 2 months, 2 weeks ago

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