Question

root3 - 1 upon root 3 +1 =a+broot 3

Answer 1

Answer:

Values of a = 2 and b = -1

Step-by-step explanation:

Given $LHS =\frac{\sqrt{3}-1}{\sqrt{3}+1}$

/*multiply numerator and denominator by $\sqrt{3}-1$,we get

=$\frac{(\sqrt{3}-1)(\sqrt{3}-1)}{(\sqrt{3}+1)(\sqrt{3}-1)}$

=$\frac{(\sqrt{3}-1)^{2}}{(\sqrt{3})^{2}-1^{2}}$

/* By algebraic identity:

(a+b)(a-b) = a²-b² */

=$\frac{(\sqrt{3})^{2}+1^{2}-2\times \sqrt{3}\times 1}{3-1}$

\* By algebraic identity:

(a-b)² = a²+b²-2ab *\

=$\frac{3+1-2\sqrt{3}}{2}$

=$\frac{4-2\sqrt{3}}{2}$

=$\frac{2(2-\sqrt{3})}{2}$

/* After cancellation, we get

= $2-\sqrt{3}$

=$2+(-1)\sqrt{3}$ --(1)

= $a+b\sqrt{3}$----(2)

\* given RHS *\

Compare (1)& (2) , we get

a = 2 , b = -1

Therefore,

Values of a = 2 and b = -1

•••••

Answer 2

Step-by-step explanation:

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