Math, asked by YardBouy, 4 months ago

(√2+√3) / (3√2-2√3) = a -b√6 find a,b​

Answers

Answered by Anonymous
2

Question :

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

then find a and b

Answer :

Given :

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

To find :

The value of a and b

According to the question,

 \sf{ \dfrac{ \sqrt{2}  +  \sqrt{3} }{3 \sqrt{2}  - 2 \sqrt{3} } = a - b \sqrt{6}  } \\  \\  \sf{ \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} }  = a - b \sqrt{6} } \\  \\  \sf{ \dfrac{ \sqrt{2} (3 \sqrt{2}  + 2 \sqrt{3} ) +  \sqrt{3} (3 \sqrt{2} + 2 \sqrt{3})  }{18 - 12} } \\  \\  \sf{ \dfrac{6 + 2 \sqrt{6} + 3 \sqrt{6}  + 6 }{6} = a - b \sqrt{6}  } \\  \\  \sf{ \dfrac{12 + 5 \sqrt{6} }{6}  = a  - b \sqrt{6} } \\  \\  \sf{  \cancel\dfrac{12}{6}  \:  {}^{2}  +   \bigg( - \dfrac{ 5 \sqrt{6} }{6}  \bigg) = a - b \sqrt{6} } \\  \\  \sf{ 2 +  \bigg( \frac{ - 5 \sqrt{6} }{6} \bigg) = a - b \sqrt{6}  } \\  \\  \therefore {\boxed {\sf \red{a = 2 , \:  \: \: b =   - \dfrac{ 5}{6} }}}

Answered by Sly01
15

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