Math, asked by craigandrewandy4680, 1 year ago

If a,b are rational numbers find value of a,b Root3+root2 by root3-root2=a+b root6

Answers

Answered by DaIncredible
7
Identities used :

 {(a + b)}^{2}  =  {a}^{2}  +  {b}^{2}  + 2ab \\ (a + b)(a - b) =  {a}^{2}  -  {b}^{2}

Now,

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

L.H.S,

On rationalizing the denominator we get,

 =  \frac{ \sqrt{3} +  \sqrt{2}  }{ \sqrt{3}  -  \sqrt{2} }  \times  \frac{ \sqrt{3} +  \sqrt{2}  }{ \sqrt{3}  +  \sqrt{2} }  \\  \\  =  \frac{ {( \sqrt{3} )}^{2}  +  {( \sqrt{2} )}^{2}  + 2( \sqrt{3})( \sqrt{2} ) }{ {( \sqrt{3} )}^{2}  -  {( \sqrt{2}) }^{2} }  \\  \\  =  \frac{3 + 2 + 2 \sqrt{6} }{3 - 2}  \\  \\  = 5 + 2 \sqrt{6}

On comparing L.H.S and R.H.S we get,

5 + 2 \sqrt{6}  = a + b \sqrt{6}  \\  \\ a = 5 \:  :  \: b = 2

nancyyy: :slow_claps:
siddhartharao77: :-)
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