InterviewSolution
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InterviewSolution
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यदि `alpha ` व `beta ` समीकरण `ax^(2)+bx+c =0` के मूल है तो `lim_(xto(1)/(alpha))sqrt((1-cos (cx^(2)+bx+a))/(2(1-alphax)^(2)))` का मान ज्ञात कीजिए। |
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Answer» प्रश्नानुसार `alpha ` व `beta ` समीकरण `ax^(2)+bx+c=0` के मूल है। `implies` समीकरण `cx^(2)+bx+a=0` के मूल `1/alpha`व `1/beta` होंगे `impliescx^(2)+bx+a=c(c-(1)/(alpha))(x-(1)/(beta))` `thereforelim_(xto(1)/(alpha))sqrt(1-cos(cx^(2)+bx+a))=lim_(xto(1)/(alpha))sqrt(1-cos {c(x-(1)/(alpha))(x-(1)/(beta))})` `=lim_(xto(1)/(alpha))|(sin {(c)/(2)(x-(1)/(alpha))(x-(1)/(beta))})/((1-alphax))|` `=lim_(xto(1)/(alpha))|(sin {(c)/(2)(x-(1)/(alpha))(x-(1)/(beta))})/(c/2(x-(1)/(alpha))(x-(1)/(beta)))*(c (alphax-1)(betax-1))/(2 alphabeta(1-alpha x))|` `=|(c)/(2 alpha beta)((beta)/(alpha)-1)|=|(c)/(2alpha)((1)/(alpha)-(1)/(beta))|` |
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