Question

x/\4 +1 /2x/\2 = 41 /9 solve for x by using the properties of proportion

Answer 1

Value of x is 3 by using the properties of proportion.

Given

To solve the equation and find the value of "x" by using the properties of proportion.

Above equation can be solved by using componendo and dividendo theorem to find the value of x.

                             $\begin{equation}\frac{x^{4}+1}{2 x^{2}}=\frac{41}{9}\end$

By using componendo-Dividendo theorem. above equation becomes,

                             $\begin{equation}\frac{x^{4}+1+2 x^{2}}{x^{4}+1-2 x^{2}}=\frac{41+9}{41-9}\end$  

                            $\begin{equation}\frac{\left(\left(x^{2}\right)^{2}+2 x^{2}+1\right)}{\left(\left(x^{2}\right)^{2}-2 x^{2}+1\right)}=\frac{41+9}{41-9}\end$

Above equation is in $( a+b)^2$ $= a^2+b^2+2ab$ form, by applying the formula,

                             $\frac{(x^{2}+1)^2}{(x^2-1)^2} = \frac{50}{32}$

                             $\frac{(x^{2}+1)}{(x^{2}-1)} = \sqrt{\frac{50}{32} }$

                             $\frac{(x^{2}+1)}{(x^{2}-1)} = \frac{5\sqrt{2} }{4\sqrt{2} }$

                             $\frac{(x^{2}+1)}{(x^{2}-1)} = \frac{5}{4} . \frac{\sqrt{2} }{\sqrt{2} }$

                             $\frac{(x^{2}+1)}{(x^{2}-1)} = \frac{5}{4}$

Again by componendo-Dividendo theorem,

                             $\frac{x^{2}+1+x^{2} -1 }{x^{2}-1-x^{2}-1 } = \frac{5}{4}$

                                 $\frac{2x^{2} }{2} = \frac{5+4}{5-4}$

                                   $x^{2} = \frac{9}{1}$

                                   $x^{2} = 9$

                                   $x=\sqrt{9}$

                                   $x=3$  

Therefore, value of $x$ is 3.  

To learn more...

brainly.in/question/4024744                                                                                    

                       

           

Answer 2

Step-by-step explanation:

hope you will understand this,....