If x1,x2,x3 are the abscissa of the points A1, A2, A3 respectively where the lines y=m1x,y=m2x,y= m3 x meet the line 2x−y+3=0 such that m1, m2, m3 are in A.P., thenx1,x2,x3, are in
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a
A.P.
b
G.P.
c
H.P.
d
none of these
answer is C.
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Detailed Solution
We have x1=3m1−2,x2=3m2−2,x3=3m3−2⇒ 1x1+1x3=m1−2+m3−23=m1+m3−43=2m2−43=2x2(as m1, m2, m3 are in A.P.)x1,x2,x3 are in H.P.