Question

rozwiąż w łatwy sposób układ równań

8xy=-3

2yz=-3

8xz=9

Answer 1

-3xy=xz/:y  y≠0

-3y=z

2y*(-3y)=-3

-6y²=-3/:(-6)

y²=1/2

y=√2/2 v y=-√2/2

z=-3√2/2 v y=3√2/2

8x*√2/2=-3

4√2x= -3 /:4√2

x=-3√2/8 v x=3√2/8

Answer 2

8 xy = - 3

2 yz = - 3

8 x z = 9

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8 xy = 2 yz / : y

8 x = 2 z

z = 4 x

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8 x *(4 x) = 9

32 x^2 = 9

x^2 = 9/32

x = - 3/(4 p(2)) = - 3p(2)/8    lub  x = 3p(2)/8

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z = 4 x = - 3/p(2) = - (3/2) p(2)    lub   z = (3/2) p(2)

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y =  -3 / (2z)

y = - 3 / ( -3 p(2)) = 1/p(2) = p(2)/2  lub   y = - p(2)/2

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Odp.

x = - 3 p(2) / 8  ;  y = p(2)/2 ;  z = (-3/2) p(2)

lub

x = 3 p(2)/8 ;       y = - p(2)/2 ; z = (3/2) p(2)

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