Question

please give me answer​

Answer 1

Question:

If $\displaystyle{\sf\:\sqrt{3}\:x\:-\:2\:=\:2\:\sqrt{3}\:+\:4\:}$, then the value of x is

$\displaystyle{\sf\:a)\:2\:(\:1\:-\:\sqrt{3}\:)}$

$\displaystyle{\sf\:b)\:2\:(\:1\:+\:\sqrt{3}\:)}$

$\displaystyle{\sf\:c)\:1\:+\:\sqrt{3}\:}$

$\displaystyle{\sf\:d)\:1\:-\:\sqrt{3}\:}$

Answer:

The value of x is

$\displaystyle{\boxed{\red{\sf\:x\:=\:2\:(\:1\:+\:\sqrt{3}\:)}}}$.

Option b)

Step-by-step-explanation:

We have given that,

$\displaystyle{\sf\:\sqrt{3}\:x\:-\:2\:=\:2\:\sqrt{3}\:+\:4\:}$

We have to find the value of x.

Now,

$\displaystyle{\sf\:\sqrt{3}\:x\:-\:2\:=\:2\:\sqrt{3}\:+\:4\:}$

$\displaystyle{\implies\sf\:\sqrt{3}\:x\:=\:2\:\sqrt{3}\:+\:4\:+\:2}$

$\displaystyle{\implies\sf\:\sqrt{3}\:x\:=\:2\:\sqrt{3}\:+\:6}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{2\:\sqrt{3}\:+\:6}{\sqrt{3}}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{(\:2\:\sqrt{3}\:+\:6\:)\:\times\:\sqrt{3}}{\sqrt{3}\:\times\:\sqrt{3}}\:\quad\:-\:-\:-\:[\:Rationalising\:the\:denominator\:]}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{2\:\times\:3\:+\:6\:\sqrt{3}}{3}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{6\:+\:6\:\sqrt{3}}{3}}$

$\displaystyle{\implies\sf\:x\:=\:\dfrac{\cancel{6}\:(\:1\:+\:\sqrt{3}\:)}{\cancel{3}}}$

$\displaystyle{\implies\underline{\boxed{\red{\sf\:x\:=\:2\:(\:1\:+\:\sqrt{3}\:)}}}}$

∴ The value of x is

$\displaystyle{\boxed{\red{\sf\:x\:=\:2\:(\:1\:+\:\sqrt{3}\:)}}}$.