Question

If √3+1/√3-1= a+b√3. Find the value of a and b.

Answer 1

$\Large{\underline{\underline{\mathfrak{\tt{\red{Question}}}}}}$

If √3+1/√3-1= a+b√3. Find the value of a and b.

$\Large{\underline{\underline{\mathfrak{\tt{\red{Solution}}}}}}$

$\Large{\underline{\mathfrak{\tt{\orange{Given}}}}}$

• √3+1/√3-1= a+b√3

$\Large{\underline{\mathfrak{\tt{\orange{Find}}}}}$

• Value of a & b

$\Large{\underline{\underline{\mathfrak{\tt{\red{Explanation}}}}}}$

We have,

$:\mapsto\tt{\:(a+b\sqrt{3})\:=\:\dfrac{(\sqrt{3}+1)}{(\sqrt{3}-1)}} \\ \\ \small\tt{\green{\:Rationalize\:denominator}} \\ \\ :\mapsto\tt{\:(a+b\sqrt{3})\:=\:\dfrac{(\sqrt{3}+1)(\sqrt{3}+1)}{(\sqrt{3}-1)(\sqrt{3}+1)}} \\ \\ \small\tt{\green{\:\:\:\:\:\:\star\:(x+y)^2\:=\:x^2+y^2+2xy}} \\ \\ \small\tt{\green{\:\:\:\:\:\:\star\:(x^2-y^2)\:=\:(x+y)(x-y)}} \\ \\ :\mapsto\tt{\:(a+b\sqrt{3})\:=\:\dfrac{(\sqrt{3})^2+2\sqrt{3}+1}{(\sqrt{3})^2-1^2}} \\ \\ :\mapsto\tt{\:(a+b\sqrt{3})\:=\:\dfrac{3+2\sqrt{3}+1}{3-1}} \\ \\ :\mapsto\tt{\:(a+b\sqrt{3})\:=\:\dfrac{2(\sqrt{3}+2)}{2}} \\ \\ :\mapsto\tt{\:(a+b\sqrt{3})\:=\:(2+\sqrt{3})}$

Compare both side,

Since, We find here,

$:\mapsto\tt{\orange{\:Value\:of\:a\:=\:2}} \\ \\ :\mapsto\tt{\orange{\:Value\:of\:b\:=\:1}}$

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