20×23=460 21×22=462 With a little knowledge about quadratics and how multiplicated neighbours behave you know 460×462+1 = 461^2 This is because 460×462= 460×460+460+460 And 461^2= 460×460+460+461 So with the calculation of the first 2 mentioned calculation you will have an answer in less than a minute
Consider this. Square root of any four consecutive numbers plus 1 will have same solution. With this if question is sqr-root((50x51x52x53)+1) In this case x=50 And answer again will be : x(x + 3) + 1 Meaning : 50 x 53 + 1 = 2651
Why bust your butt? Use a shortcut, instead. Two shortcuts for √(ABCD+1) where A, B, C, and D are positive consecutive integers: 1. AD + 1 2. BC - 1 In this problem both result in 461. FUN FACT: any four positive consecutive integers multiplied and added to one result in a perfect square. For example: 2 x 3 x 4 x 5 + 1 = 121. 11^2 = 121.Try it with your own example. 😀
😂absolutely...this guy unnecessarily complicates materials to prove him to be some extraordinary fellow. Rather, to prove that, I have given him some tougher mathematics sums to solve. Lets see how much guts he has.
Just imagine the question had been sqrt(2023 * 2024 * 2025 * 2026 + 1) . You'd need a calculator with a 13 digit display to do the calculation. We now know the answer will be 2023^2 + 3*2023 + 1. This is MUCH easier!!! When done "by hand", do you really want to take the square root of a 13 digit number?? If calculators were allowed, don't forget that they may introduce floating point errors when doing square roots of numbers this big.
Sqrt(x(x+1)(x+2)(x+3)+1) = x^2 + 3x+1. Let x=20, RHS = 461. I trained my kids with the above formula when they are in elementary school. They all were qualified for USAMO.
This is Coolie work!!
20×23=460
21×22=462
With a little knowledge about quadratics and how multiplicated neighbours behave you know 460×462+1 = 461^2
This is because 460×462= 460×460+460+460
And 461^2= 460×460+460+461
So with the calculation of the first 2 mentioned calculation you will have an answer in less than a minute
🗨️👀
Am sured that you are mostly following or solving problems similar to explored maths and also editing such as like or subscribe BUTTONS
Best of LUCK 🤞
Simple and elegant.
Thanks...❣️❣️
the GUY operating @explored maths is so GENIOUS and solving questions authenticaticlly
Consider this. Square root of any four consecutive numbers plus 1 will have same solution.
With this if question is
sqr-root((50x51x52x53)+1)
In this case x=50
And answer again will be : x(x + 3) + 1
Meaning : 50 x 53 + 1 = 2651
Yes, you are right......
I realized this on my own about half an hour ago. ROFL
What I am now wondering is: If there is an even number of sequential integers (plus "1"), is the solution always FIRST times LAST, plus 1?
Or maybe a multiple of four sequential integers?
21x22 - 1 = 462 - 1 = 461
461
Yes....
Why bust your butt? Use a shortcut, instead. Two shortcuts for √(ABCD+1) where A, B, C, and D are positive consecutive integers:
1. AD + 1
2. BC - 1
In this problem both result in 461.
FUN FACT: any four positive consecutive integers multiplied and added to one result in a perfect square. For example:
2 x 3 x 4 x 5 + 1 = 121. 11^2 = 121.Try it with your own example. 😀
😂absolutely...this guy unnecessarily complicates materials to prove him to be some extraordinary fellow. Rather, to prove that, I have given him some tougher mathematics sums to solve. Lets see how much guts he has.
just do the calculation rather than wasting all this time
Ok
That's no fun!
@@jancie202 How...?
Just imagine the question had been sqrt(2023 * 2024 * 2025 * 2026 + 1) . You'd need a calculator with a 13 digit display to do the calculation. We now know the answer will be 2023^2 + 3*2023 + 1. This is MUCH easier!!!
When done "by hand", do you really want to take the square root of a 13 digit number??
If calculators were allowed, don't forget that they may introduce floating point errors when doing square roots of numbers this big.
The formula x^2 + 3x + 1 can be rewritten as x(x+3)+1. This means the final answer to the question I introduced is: 2023 * 2026 + 1. Much faster!!!!!
It’s stupid to introduce y
So, what's not stupid... ???
Sqrt(x(x+1)(x+2)(x+3)+1) = x^2 + 3x+1. Let x=20, RHS = 461. I trained my kids with the above formula when they are in elementary school. They all were qualified for USAMO.
Weldon....👍👍❣️❣️❣️