Happy Valentines Day ♡ \heartsuit It's only YOU and ME

Algebra Level 2

{ Y O U + M E = 1 Y O U × M E = 3 Y O U − M E = ? \begin{cases} YOU + ME =1 \\ YOU \times ME=3 \\ YOU-ME=? \end{cases}

Clarification: Y O U YOU and M E ME are two numbers.

This is a submission to Valentines Day Celebration Contest .
Nothing i.e. 0 0 You don't care i.e. Y O U YOU It's still the same i.e. Y O U + M E YOU+ME Non-real answer

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Sandeep Bhardwaj by Sandeep Bhardwaj , 28, India

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2 solutions

Michael Fuller
Feb 14, 2016

Let Y O U = a YOU=a and M E = b ME=b . Then a + b = 1 a+b=1 and a b = 3 ab=3 .

⇒ ( a + b ) 2 = a 2 + b 2 + 2 a b = a 2 + b 2 + 6 = 1 ⇒ a 2 + b 2 = − 5 \Rightarrow {(a+b)}^{2}=a^2+b^2+2ab=a^2+b^2+6=1 \Rightarrow a^2+b^2 = -5

Immediately, problems are arising as a 2 > 0 a^2>0 and b 2 > 0 b^2>0 , yet the right hand side is negative!

⇒ ( a − b ) 2 = a 2 + b 2 − 2 a b = − 5 − 6 = − 11 ⇒ a − b = − 11 \Rightarrow {(a-b)}^{2}=a^2+b^2-2ab=-5-6=-11 \Rightarrow a-b= \sqrt{-11}

Hence Y O U − M E YOU-ME cannot happen!

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Yes. You can solve it logically as well ;)

Nihar Mahajan - 5 years, 4 months ago

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well i do not know how you can subtract me from you

Joel Yip - 5 years, 2 months ago

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Easy. Like this: Y O U − M E YOU-ME . :eggplant:

Nihar Mahajan - 5 years, 2 months ago

YOU-ME = Cant happen! Nice thought haha :p

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