√2+√3÷3√2-2√3=a-b√6
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Question:
[tex] = > \frac{ \sqrt{2} + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } = a - b \sqrt{6} [/tex]
Answer:
[tex] = > \frac{ \sqrt{2} + \sqrt{3} }{3 \sqrt{2} - 2 \sqrt{3} } = a - b \sqrt{6} [/tex]
Rationalising L.H.S.,
[tex] = > \frac{( \sqrt{2} + \sqrt{3} )(3 \sqrt{2} + 2 \sqrt{3} ) }{18 - 12} = a - b \sqrt{6} [/tex]
[tex] = > \frac{6 + 2 \sqrt{6} + 3 \sqrt{6} + 6 }{6} = a - b \sqrt{6} [/tex]
[tex] = > 12 + 5 \sqrt{6} = 6a - 6b \sqrt{6} [/tex]
On comparing both sides,
[tex] = > 6a = 12 [/tex]
[tex] = > a = 2[/tex]
[tex] = > - 6b = 5[/tex]
[tex] = > b = \frac{ - 5}{6} [/tex]
Hope this answer helps you ^_^ !