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Plzzzz ans question no 9 fast with cimplete solution fast ​

Answer»

GIVEN:-

  • if \rm{\dfrac{\sqrt{<klux>2</klux>}-\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}=a+b\sqrt{6}}

TO FIND:-

CONCEPT USED:-

Now,

\implies\rm{\dfrac{\sqrt{2}-\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}=a+b\sqrt{6}}

\implies\rm{\dfrac{\sqrt{2}-\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}\times{\dfrac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}-2\sqrt{3}}}}

\implies\rm{\dfrac{6-2\sqrt{6}-3\sqrt{6}+6}{18-12}}

\implies\rm{\dfrac{12-2\sqrt{6}-3\sqrt{6}}{6}}

\implies\rm{\dfrac{12-5\sqrt{6}}{6}}

\implies\rm{\dfrac{12-5\sqrt{6}}{6}=a+b\sqrt{6}}

\implies\rm{\dfrac{12}{6}-\dfrac{5}{6}=a+b}

Hence, The value of a is 2 and b is -5/6.

SOME IDENTITIES

  • \rm{(a+b)^2=a^2b^2+2ab}

  • \rm{(a-b)^2=a^2-2ab+b^2}

  • \rm{a^3+b^3=(a+b)(a^2-ab+b^2)}

  • \rm{a^3-b^3=(a-b)(a^2+ab+b^2)}


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