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Question Number 23721 by Tinkutara last updated on 06/Nov/17

If symbols have their usual meaning then (1/r^2 ) + (1/r_1 ^2 ) + (1/r_2 ^2 ) + (1/r_3 ^2 ) = (1) ((a^2 + b^2 + c^2 )/s^2 ) (2) (Δ/(a^2 + b^2 + c^2 )) (3) ((a^2 + b^2 + c^2 )/Δ^2 ) (4) ((a + b + c)/Δ^2 )

$$\mathrm{If}\:\mathrm{symbols}\:\mathrm{have}\:\mathrm{their}\:\mathrm{usual}\:\mathrm{meaning} \\ $$$$\mathrm{then}\:\frac{\mathrm{1}}{{r}^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{{r}_{\mathrm{1}} ^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{{r}_{\mathrm{2}} ^{\mathrm{2}} }\:+\:\frac{\mathrm{1}}{{r}_{\mathrm{3}} ^{\mathrm{2}} }\:= \\ $$$$\left(\mathrm{1}\right)\:\frac{{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} }{{s}^{\mathrm{2}} } \\ $$$$\left(\mathrm{2}\right)\:\frac{\Delta}{{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} } \\ $$$$\left(\mathrm{3}\right)\:\frac{{a}^{\mathrm{2}} \:+\:{b}^{\mathrm{2}} \:+\:{c}^{\mathrm{2}} }{\Delta^{\mathrm{2}} } \\ $$$$\left(\mathrm{4}\right)\:\frac{{a}\:+\:{b}\:+\:{c}}{\Delta^{\mathrm{2}} } \\ $$

Answered by Tinkutara last updated on 07/Nov/17

Commented by ajfour last updated on 07/Nov/17

thank a lot.

$${thank}\:{a}\:{lot}. \\ $$

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