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 4 minus 2 square root of 6 over denominator 3 plus 4 plus 2 square root of 6 end fraction plus fraction numerator 3 plus 4 plus 2 square root of 6 over denominator 3 plus 4 minus 2 square root of 6 end fraction minus 1
equals fraction numerator 7 minus 2 square root of 6 over denominator 7 plus 2 square root of 6 end fraction plus fraction numerator 7 plus 2 square root of 6 over denominator 7 minus 2 square root of 6 end fraction minus 1
equals fraction numerator open parentheses 7 minus 2 square root of 6 close parentheses squared plus open parentheses 7 plus 2 square root of 6 close parentheses squared over denominator open parentheses 7 plus 2 square root of 6 close parentheses open parentheses 7 minus 2 square root of 6 close parentheses end fraction minus 1
equals fraction numerator 49 plus 24 minus 28 square root of 6 plus 49 plus 24 plus 28 square root of 6 over denominator 49 minus 24 end fraction minus 1
equals 146 over 25 minus 1
equals 121 over 25

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