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kati45 [8]
3 years ago
15

Help! Exponential Equation WITHOUT CALCULATOR

Mathematics
1 answer:
ale4655 [162]3 years ago
4 0

1.
(2^{x} -2^{-x})^{2} = 4^{2} \\ \\2^{2x}-2*2^{x}*2^{-x} + 2^{-2x} =4^{2} \\ \\2^{2x}-2*2^{x-x} + 2^{-2x} =4^{2} \\ \\ 2^{2x}+ 2^{-2x} - 2=16 \\ \\ 2^{2x}+ 2^{-2x} = 18

\\ \\ 2.( 2^{x})^{3} - (2^{-x}^) ^{3}= (2^{x} -2^{-x})(2^{2x}+2^{x}*2^{-x}+2^{-2x})
\\ \\ ( 2^{x})^{3} - (2^{-x}^)^{3}=(2^{x} -2^{-x})(2^{2x}+2^{-2x}+2^{x}*2^{-x})
\\ \\ ( 2^{x})^{3} - (2^{-x}^)^{3}=(2^{x} -2^{-x})(2^{2x}+2^{-2x}+1)
\\ \\ ( 2^{x})^{3} - (2^{-x}^)^{3}=(2^{x} -2^{-x})((2^{2x}+2^{-2x})+1)


\\ \\ ( 2^{x})^{3} - (2^{-x})^{3} =(4)((18)+1)= 76
\\ \\ 2^{3x}-2^{-3x} =76

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\sqrt{3Answer:

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I'm not sure if it only wants you to find Equation 1 or go further and solve:

x = the number of 5c coins

y = the number of 10c coins

Equation 1: the total number of coins is 65

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<u>Simultaneous Equations</u>

Make one coefficient the same

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Subtract the equations

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