It's only a root

Algebra Level 1

Evaluate for x:

x × 4 x 2 × 2 x = 2048 x \times \sqrt{4 x^2×2^x} = 2048


The answer is 8.

Victor Paes Plinio by Victor Paes Plinio , 21, Brazil

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2 solutions

Finn Hulse
Apr 20, 2014

Nice problem Victor.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Thanks!

Victor Paes Plinio - 7 years, 1 month ago
Danish Anwar
Apr 25, 2014

x * sqrt (4 * x^2* 2^x) =x * sqrt (2^2* x^2* 2^x)= x * sqrt (2^2 * x^2* 2^x)= x * sqrt (2^(x+2) * x^2)= x * sqrt (2^(x+2) ) sqrt( x^2) = = x * 2^(x/2+1) * x = x^2 * 2 * 2^(x/2)=2048 x^2 2^ (x/2)=1024 sqrt(x^2* 2^ (x/2))=sqrt(1024) x* 2^(x/4)=32 so the factor satisfying this equation is 8

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Yeah that was good one

ashutosh mahapatra - 7 years, 1 month ago

2√2^x * x√x^2 = 2048

2 * 2^x/2 * x^2 = 2048 now by hit and trial method

this equation satisfies x=8 :)

Tanmay Baranwal - 7 years, 1 month ago

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