Question

Aflați numerele x,y,z stiind ca sunt invers proportionale cu 1/4, 1/6 si 1/8 si suma pătratelor lor este 116.
Va rog frumos!!!

Answer 1

Răspuns:

Explicație pas cu pas:

x/4 = y/6 = z/8 = k

x = 4k

y = 6k

z = 8k

x^2 + y^2 + z^2 = 116

16k^2 + 36k^2 + 64k^2 = 116

116k^2 = 116

k^2 = 1

k = 1

x = 4; y = 6; z = 8

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k = -1

x = -4; y = -6; z = -8

Answer 2

Bună!

$x^{2} +y^{2} +z^{2} =116\\x*\frac{1}{4} =y*\frac{1}{6} =z*\frac{1}{8} =k\\\frac{x}{4} =\frac{y}{6} =\frac{z}{8} =k\\=> x=4k\\=>y=6k\\=>z=8k\\(4k)^{2} +(6k)^{2} +(8k)^{2} =116\\16k^{2} +36k^{2} +64k^{2} =116\\116k^{2} =116\\k=1\\=> x=4k=4*1=4\\=> y=6k=6*1=6\\=> z=8k=8*1=8\\sau \\k=-1\\=> x=-4\\=>y=-6\\=> z=-8$