Tag: reducing simple equations to simpler form

Questions Related to reducing simple equations to simpler form

If $\cfrac{7}{m-\sqrt{3}} = \cfrac{\sqrt{3}}{m} + \cfrac{4}{2m}$, calculate the value of $m$.

maths equation reducing simple equations to simpler form solving linear equations solution of a linear equation in one variable

  1. $-3.464$

  2. $-1.978$

  3. $-0.918$

  4. $1.978$

Show answer
Correct Option: B
Explanation:

Given $\dfrac { 7 }{ m-\sqrt { 3 }  } =\dfrac { \sqrt { 3 }  }{ m } +\dfrac { 4 }{ 2m } =\dfrac { 4+2\sqrt { 3 }  }{ 2m } $
$\Rightarrow  14m=(4+2\sqrt { 3 } )m-\sqrt { 3 } (4+2\sqrt { 3 } )$
$ \Rightarrow (10-2\sqrt { 3 } )m=-4\sqrt { 3 } -6$
$\Rightarrow  m=\dfrac { -4\sqrt { 3 } -6 }{ 10-2\sqrt { 3 }  } =\dfrac { -12.928 }{ 6.536 } =-1.98$