SOLVE THE FOLLOWING :

Asked by nisha_vini29 | 26th May, 2017, 10:49: AM

Expert Answer:

begin mathsize 14px style straight x equals fraction numerator square root of 3 minus square root of 2 over denominator square root of 3 plus square root of 2 end fraction equals fraction numerator square root of 3 minus square root of 2 over denominator square root of 3 plus square root of 2 end fraction cross times fraction numerator square root of 3 minus square root of 2 over denominator square root of 3 minus square root of 2 end fraction equals fraction numerator open parentheses square root of 3 minus square root of 2 close parentheses squared over denominator open parentheses square root of 3 close parentheses squared minus open parentheses square root of 2 close parentheses squared end fraction equals fraction numerator 3 plus 2 minus 2 square root of 6 over denominator 3 minus 2 end fraction equals 5 minus 2 square root of 6
straight y equals fraction numerator square root of 3 plus square root of 2 over denominator square root of 3 minus square root of 2 end fraction equals fraction numerator square root of 3 plus square root of 2 over denominator square root of 3 minus square root of 2 end fraction cross times fraction numerator square root of 3 plus square root of 2 over denominator square root of 3 plus square root of 2 end fraction equals fraction numerator open parentheses square root of 3 plus square root of 2 close parentheses squared over denominator open parentheses square root of 3 close parentheses squared minus open parentheses square root of 2 close parentheses squared end fraction equals fraction numerator 3 plus 2 plus 2 square root of 6 over denominator 3 minus 2 end fraction equals 5 plus 2 square root of 6

left parenthesis straight i right parenthesis space straight x squared plus xy plus straight y squared equals open parentheses 5 minus 2 square root of 6 close parentheses squared plus open parentheses 5 minus 2 square root of 6 close parentheses open parentheses 5 plus 2 square root of 6 close parentheses plus open parentheses 5 plus 2 square root of 6 close parentheses squared
equals left parenthesis 25 plus 24 minus 20 square root of 6 right parenthesis plus left parenthesis 25 minus 24 right parenthesis plus left parenthesis 25 plus 24 plus 20 square root of 6 right parenthesis
equals 49 minus 20 square root of 6 plus 1 plus 49 plus 20 square root of 6
equals 99 end style
 
As, we have rationalise the denominators of x and y to get the desired result.
Now, we would appreciate if you can solve the 2nd sub-question and post your solution to us.

Answered by Rashmi Khot | 26th May, 2017, 12:28: PM