Question

if x=5-√3/5+√3and y=5+√3/5-√3 show that x^2-y^2=-10/11√3

Answer 1

x+y=5+3​5−3​​+5−3​5+3​​=(5−3​)(5+3​)(5−3​)2+(5+3​)2​=52−(3​)22(52+(3​)2)​=25−32(25+3)​=1128​x−y=5+3​5−3​​−5−3​5+3​​=52−(3​)2(5−3​)2−(5+3​)2​=25−32(−2×5×3​)​=−11103​​​ 
Hope u like the process
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\begin{lgathered}{x}^{2} - {y}^{2} = (x - y)(x + y) \\ = - \frac{10 \sqrt{3} }{11} \times \frac{28}{11} = - \frac{280 \sqrt{3} }{121}\end{lgathered}x2−y2=(x−y)(x+y)=−11103​​×1128​=−1212803​​​