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solve-2-x-3-x-5-x-




Question Number 167682 by bounhome last updated on 22/Mar/22
solve: 2^x +3^x =5^x
$${solve}:\:\mathrm{2}^{{x}} +\mathrm{3}^{{x}} =\mathrm{5}^{{x}} \\ $$
Commented by mr W last updated on 22/Mar/22
is it not to see that x=1?
$${is}\:{it}\:{not}\:{to}\:{see}\:{that}\:{x}=\mathrm{1}? \\ $$
Answered by HeferH last updated on 22/Mar/22
    2^x  = 5^x  − 3^x    1 = (((3 + 2)/2))^x  − ((3/2))^x     ((3/2))^x  + 1 = ((3/2) + 1)^x       x = 1
$$\: \\ $$$$\:\mathrm{2}^{{x}} \:=\:\mathrm{5}^{{x}} \:−\:\mathrm{3}^{{x}} \\ $$$$\:\mathrm{1}\:=\:\left(\frac{\mathrm{3}\:+\:\mathrm{2}}{\mathrm{2}}\right)^{{x}} \:−\:\left(\frac{\mathrm{3}}{\mathrm{2}}\right)^{{x}} \\ $$$$\:\:\left(\frac{\mathrm{3}}{\mathrm{2}}\right)^{{x}} \:+\:\mathrm{1}\:=\:\left(\frac{\mathrm{3}}{\mathrm{2}}\:+\:\mathrm{1}\right)^{{x}} \: \\ $$$$\:\:\:{x}\:=\:\mathrm{1} \\ $$$$\:\:\: \\ $$
Commented by Rasheed.Sindhi last updated on 23/Mar/22
Good saying!
$$\mathcal{G}{ood}\:{saying}! \\ $$
Commented by mr W last updated on 23/Mar/22
it′s easier to make easy things  complex than to make complex  things easy.
$${it}'{s}\:{easier}\:{to}\:{make}\:{easy}\:{things} \\ $$$${complex}\:{than}\:{to}\:{make}\:{complex} \\ $$$${things}\:{easy}. \\ $$

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