Question

If 5-√3/2+√3=x+y√3 then find x and y​

Answer 1

Answer:

Step-by-step explanation:

5-√3/2+√3=x+y√3

LHS=

5-√3/2+√3

=5-√3/2+√3×2-√3/2-√3

=(5-√3)(2-√3)/(2)² - (√3)²

=5(2-√3)-√3(2-√3)/4-3

=10-5√3-2√3+3/1

=10+3-5√3-2√3/1

=13-7√3/1

ON COMPARING,

a=13

b= 7

Answer 2

Answer:

The answer is $x=13,y=-7$

Step-by-step explanation:

Given

        $\dfrac{5-\sqrt 3}{2+\sqrt 3}=x+y\sqrt 3$

Rationalize denominator of LHS

   $\Rightarrow \dfrac{5-\sqrt 3}{2+\sqrt 3}\times \dfrac{2-\sqrt 3}{2-\sqrt 3}=x+y\sqrt 3\\\\\Rightarrow \dfrac{10-5\sqrt 3-2\sqrt 3+(\sqrt 3)^2}{2^2-(\sqrt 3)^2}=x+y\sqrt 3\\\\\Rightarrow \dfrac{10-7\sqrt 3+3}{4-3}=x+y\sqrt 3\\\Rightarrow 13-7\sqrt 3=x+y\sqrt 3$

Thus $x=13,y=-7$