I Got this Question from my maths teacher.. Plz help.!!
X^1/3 + x^1/2 =12
I got the answer 64.. but by hit n trial, a meaningful one at that..but still show me how to solve it..PLZ!
what u have done is factored.. but u did use hit and trial somewhere.. is there NO proof which boils down to x=64..?
Do u have to put 2 as u or x^1/3
to get the answer :S ?
P.s. i did the same thing.
what i did is:
x^1/2 + x^1/3 =12
since rhs is rational lhs has to be rational.
there for x has to be m^3 and n^ 2
min. value is when x=m^6
trying 1, we get 2.
trying 2 we get the answer.
trying 3, we exceed.
But since the Q includes cube root, we must try negative value,
trying -1, we get 0
trying -2, we get -4
trying -3, we exceed.
so 2 is the only real ans.