Quizzes A funny algebra puzzle!

A funny algebra puzzle!

KCC

on Feb 20, 2023

a and b are real numbers

We have the following expressions:

a² - b² = 9

a.b = 3

Question: what are the value(s) for a and b ?

Good luck! And try to be among the first ones!

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[edited by: emassa at 2:37 PM (GMT -5) on 20 Feb 2023]

Tags: algebra puzzle brainstorming enigma AQQ228 KCC KCC's Quizzes Show More

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ricardohabre

over 1 year ago
a = +- 3.1477

b = +- 0.953
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FonsJ

over 1 year ago in reply to ricardohabre
a²-b² = 9 => b² = a²-9
a.b = 3 => b = 3/a => b² = 9/a²
a²-9=9/a²
a4-9a²-9 = 0
(a²-4.5)²-20.25-9=0
a²-4.5 = SQRT(29.25)
a = SQRT(SQRT(29.25)+4.5) = 3.1477, b = 3/a = 0.9530
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FonsJ

over 1 year ago in reply to ricardohabre
a²-b² = 9 => b² = a²-9
a.b = 3 => b = 3/a => b² = 9/a²
a²-9=9/a²
a4-9a²-9 = 0
(a²-4.5)²-20.25-9=0
a²-4.5 = SQRT(29.25)
a = SQRT(SQRT(29.25)+4.5) = 3.1477, b = 3/a = 0.9530
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KCC

over 1 year ago in reply to FonsJ
Many thanks Fons! It's indeed a little bit more complex with the dot line in a.b not being a simple decimal point...As stated for Gaetano, the final answer will be confirmed in a few days...
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