Solve-by-computer-programing-if-possible-d-lt-a-lt-b-amp-c-lt-a-b-gt-2c-a-2-b-2-5c-2-2d-2-a-b-c-d-N-c-2-d-2-a-2-i-2c-2-d-2-

Question Number 188442 by BaliramKumar last updated on 03/Mar/23

Solve by computer programing (if possible) d<a<b & c < a, b>2c a^2 +b^2 = 5c^2 +2d^2 (a, b, c, d ∈ N) c^2 +d^2 = a^2 .........(i) (2c)^2 +d^2 = b^2 .........(ii) (a, b, c, d) = ?

$$ \\ $$$${Solve}\:{by}\:{computer}\:{programing} \\ $$$$\left({if}\:{possible}\right)\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:{d}<{a}<{b}\:\&\:{c}\:<\:{a},\:{b}>\mathrm{2}{c} \\ $$$$\cancel{{a}^{\mathrm{2}} +{b}^{\mathrm{2}} =\:\mathrm{5}{c}^{\mathrm{2}} +\mathrm{2}{d}^{\mathrm{2}} }\:\:\:\:\:\:\:\:\:\:\:\:\left({a},\:{b},\:{c},\:{d}\:\:\in\:\mathrm{N}\right) \\ $$$${c}^{\mathrm{2}} +{d}^{\mathrm{2}} \:=\:{a}^{\mathrm{2}} \:\:\:\:\:\:\:\:………\left({i}\right) \\ $$$$\left(\mathrm{2}{c}\right)^{\mathrm{2}} +{d}^{\mathrm{2}} \:=\:{b}^{\mathrm{2}} \:\:………\left({ii}\right) \\ $$$$ \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\left({a},\:{b},\:{c},\:{d}\right)\:=\:? \\ $$

Answered by nikif99 last updated on 02/Mar/23