Question

if (√2+√3)/(3√2-2√3)=x+√6y,find x and y​

Answer 1

Thanks for A2A

The given number is 2–√+3–√32–√–23–√

Notice that 32–√–23–√=9∗2−−−−√−4∗3−−−−√

=18−−√−12−−√=6–√(3–√−2–√) . Using this our given number becomes:

2–√+3–√32–√–23–√=3–√+2–√6–√(3–√−2–√)

Rationalising the denominator gives us:

2–√+3–√32–√–23–√=(3–√+2–√)26–√ . Which further simplifies to :

2–√+3–√32–√–23–√=56–√6+2.

Comparing with a+b6–√ gives us:

b=56 and a=2

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