exercise for ur brain..!!!

a triangle is constructed using wires ..ab, bc,ca of same material and of resistance ....alpha ,2alpha,3alpha rescptivly....Another wire of resistance alpha/3 frm A can make sliding contact wid wire BC . find maximum resistance of network btn points A and the point of sliding wire wid BC.

read only after u hv tried ths q atleast once..!!!

i solved it ....by first assuming their lengths l, 2l, 3l...thn assumend tht BC is divided into x and 2l-x whn eqv resistance is maximum...thn i wrote eqv resistance in terms of x and differentiate and thn equating to zero.....but i got a cubic in x ...and it didn give me any ans...

after reading ths plz tell me wht is my mistake...