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Question Number 200066 by hardmath last updated on 13/Nov/23
If   ((1 + x)/( (√3))) = 3   find   x + (1/x) − 1 = ?
$$\mathrm{If}\:\:\:\frac{\mathrm{1}\:+\:\mathrm{x}}{\:\sqrt{\mathrm{3}}}\:=\:\mathrm{3}\:\:\:\mathrm{find}\:\:\:\mathrm{x}\:+\:\frac{\mathrm{1}}{\mathrm{x}}\:−\:\mathrm{1}\:=\:? \\ $$
Answered by Frix last updated on 13/Nov/23
x=−1+3(√3) ⇒ (1/x)=((1+3(√3))/(26)) ⇒ x+(1/x)−1=((−51+81(√3))/(26))
$${x}=−\mathrm{1}+\mathrm{3}\sqrt{\mathrm{3}}\:\Rightarrow\:\frac{\mathrm{1}}{{x}}=\frac{\mathrm{1}+\mathrm{3}\sqrt{\mathrm{3}}}{\mathrm{26}}\:\Rightarrow\:{x}+\frac{\mathrm{1}}{{x}}−\mathrm{1}=\frac{−\mathrm{51}+\mathrm{81}\sqrt{\mathrm{3}}}{\mathrm{26}} \\ $$
Commented by hardmath last updated on 13/Nov/23
answer: a)6 b)7 c)8 d)11 e)12
$$\left.\mathrm{a}\left.\mathrm{n}\left.\mathrm{s}\left.\mathrm{w}\left.\mathrm{er}:\:\mathrm{a}\right)\mathrm{6}\:\mathrm{b}\right)\mathrm{7}\:\mathrm{c}\right)\mathrm{8}\:\mathrm{d}\right)\mathrm{11}\:\mathrm{e}\right)\mathrm{12} \\ $$
Commented by Frix last updated on 13/Nov/23
Can you find an error in my calculation?
$$\mathrm{Can}\:\mathrm{you}\:\mathrm{find}\:\mathrm{an}\:\mathrm{error}\:\mathrm{in}\:\mathrm{my}\:\mathrm{calculation}? \\ $$

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