Can you Simplify the Expression without using a Calculator | 80% Failed to solve!
2024 ж. 9 Мам.
1 758 Рет қаралды
Also Watch our Most Viral Interesting Math Olympiad Problem:
• Math Olympiad | A Nice...
Subscribe to our channel and press the bell icon 🔔 for daily Brainstorming Math videos →
/ @vijaymaths5483
*****************************************************************************
#matholympiad #maths #exponential #radical
Enjoyed watching..Thanks 👍
Before you squared both sides you could see the thing under the square root simplifies to (a^2+3a+1)^2 and cancel the square with the square root
Drastically too complicated for me, at least. At my rate of slip errors, i would never arrive at a solution on that road. Just estimating the root to be somewhere very near 97.5^4, calculating that to the nearest integer as (97,5 ^ 2) ^2, then doing one step newton for the square root yields the result without any hassle and even with only very few digits to be corrected on the way.
9505
i think if you made ''a = 100'' is better than ''a = 96'' at first, the solution would be easier.
@nadkhaa8360 Yes. By our choice of decimal system of numbers, we acquired a certain felicity for numbers expressed as decimal numbers. So we need to convert them accordingly. For the time being, remove the √sign and consider the number under it. (96 X 97 X 98 X 99)+1 = [96 X 98] X [97 X 99]+1 = [(97-1).(97+1)] X [(98-1).(98+1)]+1 = [(97^2-12).(98^2-12)]+1 = [((100-3)^2-12). ((100-2)^2-12)]+1 = [(100^2+3^2 - (2 . 100 . 3) -1). (100^2 +2^2 - (2 . 100 . 2) -1)]+1 = [(100^2 +9 -600 -1). (100^2 +4 -400 -1)]+1 = [(100^2 +8 -600). (100^2+3 -400)]+1, term by term multiplying, = [100^4 -100^2[(600-8)+(400-3)] +(592)(397) +1 = [100^4 -100^2(1000-11)+(600-8)(400-3)]+1 = 100^4-100^2(989) +(240000-((600X3)-(400X8)+24)+1 = 100,000,000-9,890,000+(240000-1800-3200+24)+1 = 100,000,000-9,890,000+240000-5000+25 = 109, 890,000+235,025 = 110,125,025. And, √[110,125,025] = 10494.04712 {Please verify for any errors}. We can do this (multiplying term by term) as [(100-4)(100-3)(100-2)(100-1)+1], also.