Question

1 + root 3 / 1 - root 3​

Answer 1

Question :-

• Here in the given equation we have to rationalize it

Answer :-

• Firstly we will multiply and divide by same number with opposite sign.

• We will also used some identities for the solution

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$\implies\sf{\dfrac{1+\sqrt{3}}{1-\sqrt{3}}}$

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$\implies\sf{\dfrac{1+\sqrt{3}\times(1+\sqrt{3})}{1-\sqrt{3}\times(1+\sqrt{3})}}$

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

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$\implies\sf{\dfrac{1+3+2\sqrt{3}}{1-3}}$

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$\implies\sf{\dfrac{4+2\sqrt{3}}{-2}}$

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$\implies\sf{\dfrac{2(2+\sqrt{3})}{-2}}$

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$\implies\sf{\dfrac{\cancel{2}(2+\sqrt{3})}{\cancel{-2}}}$

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$\implies\sf{-(2+\sqrt{3})}$

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Formula Used :-

★ $\sf{(a+b)(a+b)=\ (a+b)^{2}}$

★$\sf{(a+b)(a-b)=\ a^{2}- \ b^{2}}$

Answer 2

Answer:

a²-b² is answer of question