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If x =√3+1/√3-1 and y=√3-1/√3+1 find …

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If x =√3+1/√3-1 and y=√3-1/√3+1 find the value of x^2+xy-y^2

Posted by Bjj Ghh 6 years, 2 months ago

CBSE > Class 09 > Mathematics

1 answers

Tanisha Jain 6 years, 2 months ago

x=(√3+1/√3-1)×(√3+1/√3+1) ={(√3+1)(√3-1)}/{(√3+1)(√3+1)} ={(√3)(√3)+2(√3)(1)+(1)(1)}/{(√3)(√3)-(1)(1)} ={3+2√3+1}/{3-1} ={4+2√3}/2 =2{2+√3}/2 =2+√3 x^2={(2+√3)(2+√3)} ={(2)(2)+2(2)(√3)+(√3)(√3)} ={4+4√3+3} =7+4√3 y=(√3-1/√3+1)×(√3-1/√3-1) ={(√3-1)(√3-1)}/{(√3+1)(√3-1)} ={(√3)(√3)-2(√3)(1)+(1)(1)}/{(√3)(√3)-(1)(1)} ={3-2√3+1}/{3-1} ={4-2√3}/2 =2{2-√3}/2 =2-√3 y^2={(2-√3)(2-√3)} ={(2)(2)-2(2)(√3)+(√3)(√3)} ={4-4√3+3} =7-4√3 xy={(2+√3)(2-√3)} =(2)(2)-(√3)(√3) =4-3 =1 x^2+xy+y^2 =(7+4√3)+(1)+(7-4√3) =7+4√3+1+7-4√3 =15 Answer =15

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