Canada | A Nice Algebra Problem | Math Olympiad | 2 Methods

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14 окт 2024

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@monroeclewis1973 2 месяца назад

Many roads to Rome: Converting to exponents,first on the left: 16^1/2 x 8 1/4; (2^4) ^1/2 x (2^3) ^1/4 = 2^11/4. Then on the right: 64 ^x = (2^6)^x = 2^6x. Therefore, 2^11/4 = 2^6x. 11/4=6x. X= 11/24.

@walterwen2975 2 месяца назад

√(16√8) = 4[2^(3/4)] = 2^(2+3/4) = 2^(11/4) = 64^x = 2^6x 6x = 11/4; x = 11/24

@despa7726 2 месяца назад

sqrt(16 * sqrt(8)) = 64^x sqrt(16) * 8^(1/4) = (2^6)^x 4 * (2^3)^(1/4) = 2^6x 2^2 * 2^(3/4) = 2^6x 2^(11/4) = 2^6x 11/4 = 6x 11/24 = x

@노을-z8d 2 месяца назад

잘 보고 있습니다

@SlimEk_ 2 месяца назад

нет лол

@sie_khoentjoeng4886 2 месяца назад

√(16√8) = 64^X √(2^4√(2^3)) = (2^6) ^X √(2^4 x 2^(3/2) = 2^(6X) √(2^(11/2) = 2^(6X) 2^(11/4) = 2^6X 11/4 = 6X X = 11/24

@ogy2014 2 месяца назад

thats what i was thinking the whole time 😂

@juergenilse3259 2 месяца назад

sqrt(16*sqrt(8))=64^x (16*8^(1/2))^(1/2)=(2^6)^x (2^4*2^(3/2))^1/2)=2^(6*x) (2^(4+3/2))^(1/2)=2^(6*x) (2^(11/2))^(1/2)=2^(6*x) 2^((11/2)*(1/2))=2^(6*x) 2^(11/4)=2^(6*x) 11/4=6*x x=(11/4)/6 x=11/24

@key_board_x 2 месяца назад

√[16 * √8] = 64^(x) √[16 * √2^(3)] = 64^(x) √[16 * {2^(3)}^(1/2)] = 64^(x) √[16 * 2^(3/2)] = 64^(x) √[2^(4) * 2^(3/2)] = 64^(x) √[2^(11/2)] = 64^(x) [2^(11/2)]^(1/2) = 64^(x) 2^(11/4) = 64^(x) 2^(11/4) = [2^(6)]^(x) 2^(11/4) = 2^(6x) 11/4 = 6x x = 11/24