InterviewSolution
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InterviewSolution
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यदि `x=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2))` व `y=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))`, तब निम्न के मान ज्ञात कीजिए - `x^(2)+xy+y^(2)` |
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Answer» प्रश्नानुसार, `x=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2))` व `y=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))` हर का परिमेयीकरण करने पर `x=(sqrt(3)-sqrt(2))/(sqrt(3)+sqrt(2))xx(ssqrt(3)-sqrt(2))/(sqrt(3)-sqrt(2))=((sqrt(3)-sqrt(2))^(2))/((sqrt(3))^(2)-(sqrt(2))^(2))=(3+2-2sqrt(3)xx sqrt(2))/(3-2)=5-2sqrt(6)` और `y=(sqrt(3)+sqrt(2))/(sqrt(3)-sqrt(2))xx(sqrt(3)+sqrt(2))/(sqrt(3)+sqrt(2))=((sqrt(3)+sqrt(2))^(2))/((sqrt(3))^(2)-(sqrt(2))^(2))=(3+2+2sqrt(3)xx sqrt(2))/(3-2)=5+2sqrt(6)` इसलिए `x+y=5-2sqrt(6)+5+2sqrt(6)=10` व `xy=(5-2sqrt(6))(5+2sqrt(6))=(5)^(2)-4(sqrt(6))^(2)=25-24=1` अतः `x^(2)+xy+y^(2)=(x+y)^(2)-xy=(10)^(2)-1=99` |
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