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Question-116529




Question Number 116529 by mr W last updated on 04/Oct/20
Commented by MJS_new last updated on 04/Oct/20
(5/(197))
$$\frac{\mathrm{5}}{\mathrm{197}} \\ $$
Answered by maths mind last updated on 05/Oct/20
x^4 +4=(x^2 −2x+2)(x^2 +2x+2)  =((x−1)^2 +1)((x+1)^2 +1)  =((((2)^2 +1)(4^2 +1)(6^2 +1)(8^2 +1)(10^2 +1)(12^2 +1))/((4^2 +1)(6^2 +1)(8^2 +1)(10^2 +1)(12^2 +1)(14^2 +1)))  =(5/(197))
$${x}^{\mathrm{4}} +\mathrm{4}=\left({x}^{\mathrm{2}} −\mathrm{2}{x}+\mathrm{2}\right)\left({x}^{\mathrm{2}} +\mathrm{2}{x}+\mathrm{2}\right) \\ $$$$=\left(\left({x}−\mathrm{1}\right)^{\mathrm{2}} +\mathrm{1}\right)\left(\left({x}+\mathrm{1}\right)^{\mathrm{2}} +\mathrm{1}\right) \\ $$$$=\frac{\left(\left(\mathrm{2}\right)^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{4}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{6}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{8}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{10}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{12}^{\mathrm{2}} +\mathrm{1}\right)}{\left(\mathrm{4}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{6}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{8}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{10}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{12}^{\mathrm{2}} +\mathrm{1}\right)\left(\mathrm{14}^{\mathrm{2}} +\mathrm{1}\right)} \\ $$$$=\frac{\mathrm{5}}{\mathrm{197}} \\ $$
Commented by mr W last updated on 05/Oct/20
great!
$${great}! \\ $$

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