Math, asked by Hitlerrr71, 5 months ago

If a and b are rational number 8 then ,
find the value of a and b
→√3+√2/√3-√2=a+b√6​

Answers

Answered by SweetCharm
1

 \huge \sf {\orange {\underline {\pink{\underline{Answer :-}}}}}

  • \bigstar\bold\red{Value\:of\:a=5}
  • \bigstar\bold\red{Value\:of\:b=2}

Explanation:

\Large{\underline{\rm{Given:}}}

  • a and b are rational numbers

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

\Large{\underline{\rm{To\:Find:}}}

  • The value of a and b

\Large{\underline{\rm{Solution:}}}

Given,

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

Taking the LHS of the equation,

\sf{\dfrac{\sqrt{3} +\sqrt{2} }{\sqrt{3} -\sqrt{2} }  }

Rationalising the denominator by multiplying √3 + √2 on both numerator and denominator,

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

Simplifying by using identities:

(a + b)² = a² + b² + 2ab

(a + b) × (a - b) = a² - b²

\sf \mapsto {\dfrac{3+2+2\sqrt{6} }{3-2} }

\sf \mapsto {\dfrac{3+2+2\sqrt{6} }{1} }

\sf \mapsto {5+2\sqrt{6} }

But we know that,

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

\sf \blue{5+2\sqrt{6}=a+b\sqrt{6} }

Equating it we get,

  • a = 5
  • b = 2

Hence the value of a is 5 and value of b is 2.

{\huge{\underline{\small{\mathbb{\pink{HOPE\:HELPS\:UH :)}}}}}}

\red{\tt{sωєєтcнαям♡~}}

Answered by Anonymous
10

 \huge \sf {\orange {\underline {\pink{\underline{Answer :-}}}}}

  • \bigstar\bold\red{Value\:of\:a=5}
  • \bigstar\bold\red{Value\:of\:b=2}

Explanation:

\Large{\underline{\rm{Given:}}}

a and b are rational numbers

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

\Large{\underline{\rm{To\:Find:}}}

The value of a and b

\Large{\underline{\rm{Solution:}}}

Given,

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

Taking the LHS of the equation,

\sf{\dfrac{\sqrt{3} +\sqrt{2} }{\sqrt{3} -\sqrt{2} }  }

Rationalising the denominator by multiplying √3 + √2 on both numerator and denominator,

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

Simplifying by using identities:

(a + b)² = a² + b² + 2ab

(a + b) × (a - b) = a² - b²

\sf \mapsto {\dfrac{3+2+2\sqrt{6} }{3-2} }

\sf \mapsto {\dfrac{3+2+2\sqrt{6} }{1} }

\sf \mapsto {5+2\sqrt{6} }

But we know that,

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

\sf \blue{5+2\sqrt{6}=a+b\sqrt{6} }

Equating it we get,

a = 5

b = 2

Hence the value of a is 5 and value of b is 2.

{\huge{\underline{\small{\mathbb{\pink{HOPE\:HELPS\:UH :)}}}}}}

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