if x = √3-√2 ÷√3+√2 & y=√3+√2÷√3-2 find the value of x^2+y^2+ xy

Asked by sbjamdhade80 | 7th Jun, 2020, 06:47: PM

Expert Answer:

Given: x = √3-√2 ÷√3+√2 & y=√3+√2÷√3-2
To find the value of x2+y2+ xy
x squared plus y squared minus x y equals open parentheses fraction numerator square root of 3 minus square root of 2 over denominator square root of 3 plus square root of 2 end fraction close parentheses squared plus open parentheses fraction numerator square root of 3 plus square root of 2 over denominator square root of 3 minus square root of 2 end fraction close parentheses squared minus 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 plus square root of 2 over denominator square root of 3 minus square root of 2 end fraction
equals fraction numerator 3 plus 2 minus 2 square root of 6 over denominator 3 plus 2 plus 2 square root of 6 end fraction plus fraction numerator 3 plus 2 plus 2 square root of 6 over denominator 3 plus 2 minus 2 square root of 6 end fraction minus 1
equals fraction numerator 5 minus 2 square root of 6 over denominator 5 plus 2 square root of 6 end fraction plus fraction numerator 5 plus 2 square root of 6 over denominator 5 minus 2 square root of 6 end fraction minus 1
equals fraction numerator open parentheses 5 minus 2 square root of 6 close parentheses squared plus open parentheses 5 plus 2 square root of 6 close parentheses squared over denominator open parentheses 5 plus 2 square root of 6 close parentheses open parentheses 5 minus 2 square root of 6 close parentheses end fraction minus 1
equals fraction numerator 25 plus 24 minus 20 square root of 6 plus 25 plus 24 plus 20 square root of 6 over denominator 25 minus 24 end fraction minus 1
equals 98 minus 1
equals 97

Answered by Renu Varma | 9th Jun, 2020, 03:18: PM