Brush up your fundamentals 1

Algebra Level 5

$\left|\dfrac{x-1}{3 + 2x - 8x^{2}}\right| + \left| 1 - x \right| = \dfrac{(x -1)^{2}}{\left| 3+ 2x -8x^{2}\right|} + 1$

The solutions to the equation are of the form

$x = a , b , \dfrac{c \pm \sqrt{d}}{e} , \dfrac{ f \pm \sqrt{g}}{h}$

where $a,b,c,d,e,f,g,h$ are all positive integers, with $d$ and $g$ square-free.

Find the value of $a + b + c +d+e+f+g+ h$ .

The answer is 240.

1 solution

Shivansh Nagi
Dec 20, 2014

I think the solutions are 0,2, (3 + -sqrt 73) /16 and (1+- sqrt 129) /16. Take lcm on both sides. On simplifying we get| x-1| =| 3+2x-8x^2| and in the previous step to this we shall get| x-1| =1.

Try it, it's not that difficult. (Remember: (x-1) ^2= (1-x) ^2

Brush up your fundamentals 1

The answer is 240.

1 solution

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