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Algebra Level 2

x 3 − x 2 + 3 − x 2 x \frac {x}{\sqrt{3-x^2}} + \frac { \sqrt{3-x^2}}{x}

Find the value of the expression above if x = 3 − 5 2 x = \sqrt{ \frac {3 -\sqrt 5}{2} } .

− 3 -3 − 9 -9 6 6 3 3

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Benedict Song by Benedict Song , 19, China

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3 solutions

Aditya Chauhan
Mar 28, 2015

It is better to put the value of x at last On simplifying the eq. Becomes 3/[x√3-x^2] On putting the value of x it becomes 3/[√([3-√5]/2)([3+√5]/2)] =3/√[(9-5)/4] =3

3 Helpful 0 Interesting 0 Brilliant 0 Confused

gud but there is a more simpler way of solving this

Shashank Rustagi - 6 years, 2 months ago
Deepanshu Gupta
Mar 29, 2015

x = ϕ \displaystyle{\boxed { x=\phi } }

;)

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Zamber Blog
Mar 11, 2020

It is asked to find the value of \frac{x}{ \sqrt{ 3 - x^2}} + \frac{\sqrt{3 - x^2}}{x} at x = \sqrt{\frac{3 - \sqrt{5}}{2}}. So simplifying the value of x we get an equation x^4 -3x^2 + 1 = 0. From this we get \frac{1}{x^2} = 3 - x^2.

We can use the given value of 3 - x^2 in the original eqn. and get a simplified form of it as x^2 + \frac{1}{x^2} . Then putting x^2 = \frac{3 - \sqrt{5}}{2} in it and by taking common denominator we get x = 3.

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