RamanuGem_004_The Innocuous(looking!) pair of Equations...! :)

Hi pa...!
After a long hiatus, I am back...! :)


This time, I have decided to share another gem that was posed to a lit'l Ramanujan by a Math teacher at his school who had heard about his mathe-magical flair...!
[details may vary...I'm not exactly sure...but that's not important here..!]


Consider the below pair of equations :

Sqrt(x) + y = 7     ---> (1)
x + Sqrt(y) = 11    --->(2)


Look simple don't they..?? :)
They are deceptively like the 'simultaneous equations' in 2 unknowns viz., x & y that we all have known very well in school, right ?


Now, I request you to please grab a piece of paper, & really try solving fer x & y...& see for yourself..! :)


You will soon find that it's not so easy after all, with the brute-force method of eliminating either x or y only leading to more troubles..! Take my word fer it..!!


Hmmmmmmm...!!
Anyway, please do let me know of ANY elegant method(s) of solving this pair of equations that you may stumble upon, or KNOW already..!


The solution to the above pair...which is quite obvious, is : (x=9, & y=4)


What did lit'l Ramanujan do?--- you might ask...
Well, it is said he was ready with the answer in a jiffy ! :)
{But HOW did he approach it?? HOW did he crack it ??
I do not know; it's all shrouded in 'mist'ery...in his-story...! :)}

Love & Best Wishes,

The moRon in rags,

Planet Earth

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And here's a point to ponder...! :)

"Obvious is the most dangerous word in mathematics." 

- E.T. Bell

RamanuGem003_The amazing Ratio with Primes...! :)

I do not have too many words to say this time...i mean NOW..!
(Also because, it is freezing cold here, & i got drenched in it...& my fingers are numb, & paining...!)

But the main reason...is that...ALL my words...are embedded in the below Picture-article...that i created literally drop-by-drop...OLL day & night yesterday...sitting ALONE in my room...and trying to understand what the wind howling @ my window was trying to say to me-Moron..!!

See fer yourself..! :)

And please do let me know HOW it is...!
Will You pa..?? Hmmm...!
Isn't it PURE, SHEER Genius of the Highest ORDER...!??

Well...me jusst want to "Discover" & SHARE more & More of it, while i am here on EARTH...!

There is Genius in the Universe...in trees, insects, & even people all around...and hence, in U(s) too...it is simply thrilling to contemplate the magic in it...!!
Click on the below image to know more/WHY...

This is what i call..umm..an article that delighted my Image-ination...!! :)
{Very hard fer pagination though...! ;))}

So...without...much ado..
Here we go...! :)
























LOVE & best wishes,

the boy in "rags"
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Below is a Calvin & Hobbes strip with a nice word-play too..! ;)