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for infinitely many solutions the comparison between the ratios should be a1/a2=b1/b2=c1/c2
here a1=2
a2=k+2
b1=3
b2=b
c1=k
c2=3k+2
=2/k+2=k/3k+2
by cross multiplication
= k( k+2)=2(3k+2)
k^2+2k=6k+4
k^2+2k-6k-4
k^2-4k-4
then k= 4+4√2/2 or 4-4√2/2
here a1=2
a2=k+2
b1=3
b2=b
c1=k
c2=3k+2
=2/k+2=k/3k+2
by cross multiplication
= k( k+2)=2(3k+2)
k^2+2k=6k+4
k^2+2k-6k-4
k^2-4k-4
then k= 4+4√2/2 or 4-4√2/2
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