Consecutive members

The block has a volume of 1728 cm³. Determine the lengths of the edges a, b, and c of the blocks for which a < b < c and a + b + c = 38 cm and whose numerical values in cm represent three consecutive members of the geometric sequence.

Correct answer:

a =  8 cm
b =  12 cm
c =  18 cm

Step-by-step explanation:

V=1728 cm3  1728 = 26 × 33  V = abc b=qa c=q2a a+b+c=38  V = a aq aq2 = a3 q3 = (aq)3 a q = 3V = 31728 = 12  a aq (38aaq) = V a 12 (38a12)=V  a 12 (38a12)=1728 12a2+312a1728=0 12a2312a+1728=0 12=223 312=23313 1728=2633 GCD(12,312,1728)=223=12  a226a+144=0  p=1;q=26;r=144 D=q24pr=26241144=100 D>0  a1,2=2pq±D=226±100 a1,2=226±10 a1,2=13±5 a1=18 a2=8  a=a2=8=8 cm q=12/a=12/8=23=1.5

Our quadratic equation calculator calculates it.

b=q a=1.5 8=12 cm
c=q b=1.5 12=18 cm

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