Question

find the value of x in this question

Answer 1

Heya User,

--> Sorry for the delay but it took me quite long to write a satisfactory solution to this ..

--> However, since I have shortage of time ^_^ ,  I'll provide the basic steps for now, and will upload my answer to the satisfactory level later..

--> [ x² + [ ax / ( a + x ) ]² ] = 3a²

--> Expanded as :->
    ==> - 3a⁴ - 6a³x - a²x² + 2ax³ + x⁴ = 0
    ==  3a⁴ + 6a³x + a²x² - 2ax³ - x⁴ = 0
    ==  [ 3a⁴ + 3a³x + 3a³x - 3a²x² + 3a²x² + a²x² - 3ax³ + ax³ - x⁴ ] = 0
    ==  [ 3a⁴ + 3a³x - 3a²x² + 3a³x + 3a²x² - 3ax³ + a²x² + ax³ - x⁴ ] = 0
    ==  [ 3a⁴ + 3a³x - 3a²x² ] + [ 3a³x + 3a²x² - 3ax³ ] + [ a²x² + ax³ - x⁴ ] = 0
    ==  3a² [ a² + ax - x² ] + 3ax [ a² + ax - x² ] + x² [ a² + ax - x² ] = 0
    ==  [ a² + ax - x² ] [ 3a² + 3ax + x² ] = 0

However, the second factor gives an imaginary soln..

--> Solve for 'x' in the first factor, to get :-> 
--> $x = \frac{a + a \sqrt{5} }{2}$

And hence, you have the answer in option ( ii ) and ( iv ) ^_^

+_+ I'll provide uh with a comparatively easy and appropriate soln. pretty soon ... ATB

^_^