What base will make the bold text true:
Equation: 3x2-25x+66=0
It’s solutions x1=4 and x2=9 ?
Provide your reasoning.
Let the base be n.
Then, the given equation is:
3x^2 -(2n+5)x +(6n+6) = 0 ......($)
Since 4 is a root of the given equation, we substitute x=4 in ($) to obtain:
48-4(2n+5) +(6n+6)=0
=> 48 - 2n -14 =0
=> 2n=34
=> n=17
Accordingly, the required base seems to be 17.
So, for n=17, the equation ($) reduces to;
3x^2 - 39x+108=0 .....(#)
=> 3(x-4)(x-9)=0
=> x=4, 9
So, the two roots checks as x1=4 and x2=9 in full conformity with the provisions of the given problem.
Consequently, the required base is INDEED 17.
Puzzle Solution
