A coffin Problem

Algebra Level 4

$x(8\sqrt{1-x}+\sqrt{1+x})=11\sqrt{1+x}-16\sqrt{1-x}$

Solve the equation above for positive real $x$ .

The answer is 0.600.

1 solution

Aaghaz Mahajan
Nov 19, 2018

@Vilakshan Gupta What was your approach??? I simply found out the cubic equation and then used rational root theorem..............Also, i used RRT to check only roots between -1 and 1, so it took no time..........

@Vilakshan Gupta Also, if there would be no rational roots, then cardano's method was always there.......!!

Aaghaz Mahajan - 2 years, 6 months ago

My method is very lengthier , actually I put $x=\cos(2\theta)$ and then solved it.... I wanted another solution to it... so I posted here....

But why did you use RRT when the question doesn't says it has Rational roots?... I don't know any cardano's method...please share bro...

Can you post complete solution...

Vilakshan Gupta - 2 years, 6 months ago

@Vilakshan Gupta Heyy......sorry I read the comment just now..... :p
So, here is the link for Cardano's method, which is PRETTY COMPLICATED.........Only use it when there is no approach left.....
Also, as I mentioned before, I used RRT for the first step, because, what was the harm in checking??? right??? I mean, if RRT failed, then I would have thought of something else......but it worked......:)

Aaghaz Mahajan - 2 years, 6 months ago

A coffin Problem

The answer is 0.600.

1 solution

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