Fool's problem of the day,

If $a,b,c$ are in A.P and $a^2,b^2,c^2$ are in G.P. If $ a

Question

Fool's problem of the day,

If $a,b,c$ are in A.P and $a^2,b^2,c^2$ are in G.P. If $ a<b<c $ and  $a+b+c = \frac32$ what is the value of $a$?

An easy problem on sequence and series.

lgbasallote · Answer

a1 = a
a2 = a + (1)d = b
a3 = a + (2)d = c

a + d = b
a + 2d = c
-d = b + c
d = c -b

a1 = a^2
a2 = a^2(r)^1 = b^2
a3 = a^2(r)^2 = c^2

ra^2 = b^2
a^2(r^2) = c^2

b = a sqrt (r)
c = ar

d = ar - a sqrt (r)
d = a(r - sqrt r)
a = d/(r- sqrt r)
c - 2d = d/(r - sqrt r)
ar - 2d = d/(r - sqrt r)


okay...i give up now...i'm going in circles @_@ :P

anonymous · Answer

400 :P

anonymous · Answer

Not right experimentX

anonymous · Answer

You didnt say i was wrong :D

callisto · Answer

see right hand side

anonymous · Answer

@Ishaan94 I was thinking about you when I posted this, try it out man :)

lgbasallote · Answer

is callisto right?

anonymous · Answer

callisto's approach is right, however I would appreciate the surd as answer ;)

experimentx · Answer

1/2*(1-sqrt(2))

anonymous · Answer

Right ExperimentX

lgbasallote · Answer

oh...i was soooo close to that! lol =)))

experimentx · Answer

hahah

a+b+c=3/2
2b = a+c

and I never considered the probability that

b^2 = -ac (damn ...!)

callisto · Answer

sorry.... i can't help using the calculator... I'll leave it in the surd form next time

anonymous · Answer

I got the same but I used calculator for calculations :/