Question #25ae4

2 Answers
Nityananda · José F.
Oct 28, 2017

#5,[-5+-5isqrt(3)]/2#

Explanation:

Given,#z^3-125 = 0#
#rArr z^3-5^3 =0#
#rArr (z-5)(z^2+5z+25)=0#
#rArr (z-5)=0,(z^2+5z+25)=0#
#rArr z=5,z=[-5+-sqrt(5^2-4xx25xx1)]/(2xx1)#
#rArr z=5,z=[-5+-sqrt(-75)]/(2)#
#rArr z=5,[-5+-5isqrt(3)]/2#

Barney V.
Oct 28, 2017

#z=5#

Explanation:

#z^3-125=0#

#:.z^3=125#

cube root both sides

#:.root3(z^3)=root3(125)#

#:.root3(z*z*z)=root3(5*5*5)#

#:.root3(5)xxroot3(5)xxroot3(5)=5#

#:.root3(z)xxroot3(z)xxroot3(z)=z#

#:.z=5#

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