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

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[@monroeclewis1973]

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]

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

[@despa7726]

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

[@juergenilse3259]

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

[@user-cw8uc1ec4s]

잘 보고 있습니다

[@SlimEk_]

нет лол

[@sie_khoentjoeng4886]

√(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]

thats what i was thinking the whole time 😂

[@key_board_x]

√[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