Equalities 1

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dailymaths·Daily Maths Challengesbyscratsearcher 🔍🔮📊🎲

Equalities 1

Let a and b be rational numbers and suppose that (a-b)=4 and a*b=1 . Show that (a+b)^2 = 20.

https://hrmacbeth.github.io/math2001/01_Proofs_by_Calculation.html#proving-equalitiesOpen link View original on sopuli.xyz

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scratsearcher 🔍🔮📊🎲

sopuli.xyz

::: spoiler hint Use algebraic substitution and the binomial formulas

(a+b)^2 = a^2+2*ab+b^2

(a-b)^2 = a^2-2*ab+b^2

:::

::: spoiler Solution

(a+b)^2 = a^2 + 2*ab + b^2 = (a-b)^2 +4*ab = 4^2+4*1 = 16+4 = 20 ◽

:::

siriusmart

lemmy.world

of course the website has something to do with lean

scratsearcher 🔍🔮📊🎲 reply

sopuli.xyz

yeah I found this website quite interesting even if I dont want to learn lean right now you can learn some cool proofs. Do you mind if I post other questions from that one here?