Question

Según la figura: ²+b²+²=200 a+b+c=24 Calcula "abc​

Answer 1

Datos:

$a^{2} +b^{2} +c^{2} = 200 \\ c^{2} = a^{2} + b^{2} \\ a+b+c = 24$

$a^{2} +b^{2} +c^{2} = 200 \\ c^{2} +c^{2} = 200 \\ 2c^{2} = 200 \\ c^{2} = 100 \\ c = 10$

$a^{2} +b^{2} +c^{2} = 200 \\ a^{2} +b^{2} + 100 = 200 \\ a^{2} +b^{2} = 100 \\\\ a+b+c = 24 \\ a+b+10 = 24 \\a+b = 14 \\ a = 14-b$

$a^{2} +b^{2} = 100 \\ (14-b)^{2} + b^{2} = 100 \\ 196 -28b+b^{2} +b^{2} =100 \\ 2b^{2} -28b + 96 = 0 \\ b^{2} - 14b+48 = 0 \\ (b-6)(b-8) = 0 \\ b_{1} = 6 \\ b_{2} = 8$

$a_{1} = 14 -b_{1} \\ a_{1} = 14 - 6 \\ a_{1} = 8 \\\\ a_{2} = 14 -b_{2} \\ a_{2} = 14 - 8 \\ a_{2} = 6$

Respuesta:

$a_{1} b_{1}c = 8*6*10 \\ a_{1} b_{1}c = 480 \\\\ a_{2} b_{2}c = 6*8*10 \\ a_{2} b_{2}c = 480$