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Question Number 180837 by Mastermind last updated on 17/Nov/22

Without using table, find the values of: (1/((1−(√3))^2 )) − (1/((1+(√3))^2 )) Mastermind

$$\mathrm{Without}\:\mathrm{using}\:\mathrm{table},\:\mathrm{find}\:\mathrm{the}\:\mathrm{values} \\ $$$$\mathrm{of}: \\ $$$$\frac{\mathrm{1}}{\left(\mathrm{1}−\sqrt{\mathrm{3}}\right)^{\mathrm{2}} }\:−\:\frac{\mathrm{1}}{\left(\mathrm{1}+\sqrt{\mathrm{3}}\right)^{\mathrm{2}} } \\ $$$$ \\ $$$$\mathrm{Mastermind} \\ $$

Answered by Rasheed.Sindhi last updated on 18/Nov/22

(1/((1−(√3))^2 )) − (1/((1+(√3))^2 )) (((1+(√3))^2 −(1−(√3))^2 )/((1−(√3))^2 (1+(√3))^2 )) (({(1+(√3) )−(1−(√3) )}{(1+(√3) )+(1−(√3) )})/({(1)^2 −((√3) )^2 }^2 )) (((1+(√3) −1+(√3) )(1+(√3) +1−(√3) ))/((1−3)^2 )) (((2(√3) )(2))/2^2 ) =(√3)

$$\frac{\mathrm{1}}{\left(\mathrm{1}−\sqrt{\mathrm{3}}\right)^{\mathrm{2}} }\:−\:\frac{\mathrm{1}}{\left(\mathrm{1}+\sqrt{\mathrm{3}}\right)^{\mathrm{2}} } \\ $$$$\frac{\left(\mathrm{1}+\sqrt{\mathrm{3}}\right)^{\mathrm{2}} −\left(\mathrm{1}−\sqrt{\mathrm{3}}\right)^{\mathrm{2}} }{\left(\mathrm{1}−\sqrt{\mathrm{3}}\right)^{\mathrm{2}} \left(\mathrm{1}+\sqrt{\mathrm{3}}\right)^{\mathrm{2}} } \\ $$$$\:\frac{\left\{\left(\mathrm{1}+\sqrt{\mathrm{3}}\:\right)−\left(\mathrm{1}−\sqrt{\mathrm{3}}\:\right)\right\}\left\{\left(\mathrm{1}+\sqrt{\mathrm{3}}\:\right)+\left(\mathrm{1}−\sqrt{\mathrm{3}}\:\right)\right\}}{\left\{\left(\mathrm{1}\right)^{\mathrm{2}} −\left(\sqrt{\mathrm{3}}\:\right)^{\mathrm{2}} \right\}^{\mathrm{2}} } \\ $$$$\:\frac{\left(\mathrm{1}+\sqrt{\mathrm{3}}\:−\mathrm{1}+\sqrt{\mathrm{3}}\:\right)\left(\mathrm{1}+\sqrt{\mathrm{3}}\:+\mathrm{1}−\sqrt{\mathrm{3}}\:\right)}{\left(\mathrm{1}−\mathrm{3}\right)^{\mathrm{2}} } \\ $$$$\frac{\left(\mathrm{2}\sqrt{\mathrm{3}}\:\right)\left(\mathrm{2}\right)}{\mathrm{2}^{\mathrm{2}} } \\ $$$$=\sqrt{\mathrm{3}}\: \\ $$

Answered by Socracious last updated on 19/Nov/22

(√3)

$$\:\:\:\:\:\:\sqrt{\mathrm{3}} \\ $$

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