Question

The possible values of p and q for the equation underoot 3 -1 / underoot 3 =p+q√3​

Answer 1

Step-by-step explanation:

Given that,

$\longrightarrow\sf { \dfrac{\sqrt{3} - 1}{\sqrt{3}} = p + q\sqrt{3} }$

In order to find the value of p and q, we need to rationalise the denominator of the fraction given in the L.H.S.

In order to rationalise the denominator, we multiply the rationalising factor of denominator with both the numerator and the denominator of the fraction.

Rationalising factor of √a is √a, so rationalising factor of √3 is √3.

$\longrightarrow\sf { \dfrac{\sqrt{3} - 1}{\sqrt{3}} \times \dfrac{\sqrt{3}}{\sqrt{3}} }$

$\longrightarrow\sf { \dfrac{\sqrt{3}(\sqrt{3} - 1)}{(\sqrt{3})^2} }$

$\longrightarrow\sf { \dfrac{3 - \sqrt{3}}{3} }$

$\longrightarrow\sf { \dfrac{3}{3} - \dfrac{\sqrt{3}}{3} }$

$\longrightarrow\sf { 1 - \dfrac{1}{3} \sqrt{3} }$

On comparing L.H.S and R.H.S,

$\longrightarrow\sf { 1 + \Bigg \lgroup - \dfrac{1}{3} \Bigg \rgroup \sqrt{3} = p+q \sqrt{3} }$

∴ Value of p is 1 and value of q is -1/3.