Canada | Math Olympiad | A Nice Algebra Problem 

Really excellent. Thank you.

a^4 + b^4 + ( a + b)^4 = a^4 + b^4 + ( a^2 + b^2 + 2 a b)^2 = 2 ( a^4 + b^4 + 2 a^2 b^2 + 2 a b ( a^2 + b^2) + a^2 b^2) = 2 ( a^2 + ab + b^2) ^2 Here in a = 10, b = 9 Hereby given expression = √ (( a^4 + b^4 + ( a + b) ^4) /2) = a^2 + a b + b^2 = 100 + 90 + 81 =271

Возня ради возни. 19 в четвёртой степени я в столбик посчитаю гораздо быстрее

271

10:11 the number look familiar

Why does everyone re-write the same problem below?

What’s the point of solving it by hand when you can just punch it into a calculator?

What is the plan? Why were the numbers 81,19 and 100 used? Could it be by rearranging the terms, we have a perfect square? Please do NOT cancel the square root and square. The sq root of x squared is NOT x but the absolute value of x.

wtf why all that when you could’ve just taken off the 2 powers of all and made the calculations like: 100+81+ 19x19/ 2

Dear master, I checked the result with the calculator and it doesn’t match. It’s 91,98… not 271. What’s wrong?

271