Question

if x = 7 - 4√3 find (x^2 -1)/(x^2 +1)
answer fast i will mark brainliest and irrelevent answers be ready for report

Answer 1

Answer:

-4√3/7

Step-by-step explanation:

As per the information provided in the question, We have :

• x = 7 - 4√3

We are asked to find the value of (x^2 -1)/(x^2 +1).

In order to find the value of (x^2 -1)/(x^2 +1). We will substitute the value of x in it.

$\begin{gathered}\longmapsto \rm \dfrac{ {x}^{2} - 1 }{ {x}^{2} + 1} \end{gathered}$

Substituting the value of x.

$\begin{gathered}\longmapsto \rm \dfrac{ ({7 - 4 \sqrt{3}) }^{2} - 1 }{ {({7 - 4 \sqrt{3})}}^{2} + 1} \end{gathered}$

$\begin{gathered}\longmapsto \rm \dfrac{ ({7 - 4 \sqrt{3}) }^{2} - 1 }{ {97 - 56 \sqrt{3} + 1}} \end{gathered}$

$\begin{gathered}\longmapsto \rm \dfrac{ (97 - 56 \sqrt{3} - 1 )}{ {98 - 56 \sqrt{3} }} \end{gathered}$

$\begin{gathered}\longmapsto \rm \dfrac{ 96 - 56 \sqrt{3} }{ {98 - 56 \sqrt{3} }} \end{gathered}$

$\begin{gathered}\longmapsto \rm \dfrac{ 8(12 - 7 \sqrt{3} )}{ {14(7 - 4 \sqrt{3}) }} \end{gathered}$

$\begin{gathered}\longmapsto \rm \dfrac{4}{7} \times \dfrac{ (12 - 7 \sqrt{3} )}{ {(7 - 4 \sqrt{3}) }} \end{gathered}$

By rationalising 12-7√3/7-4√3 we get,

$\begin{gathered}\longmapsto \rm \dfrac{4}{7} \times \bigg( - \dfrac{ \sqrt{3} }{1} \bigg ) \end{gathered}$

$\begin{gathered}\longmapsto \rm - \dfrac{4 \sqrt{3} }{7} \end{gathered}$

∴ The value of (x^2 -1)/(x^2 +1) is -4√3/7.