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CBSE Class 11-science Answered

If the roots of 1/x+a + 1/x+b = 1/c are equal in magnitude but opposite in sign prove that c=a+b/2
Asked by rushabh1234 | 20 Nov, 2018, 11:19: AM
answered-by-expert Expert Answer
begin mathsize 16px style fraction numerator 1 over denominator straight x plus straight a end fraction plus fraction numerator 1 over denominator straight x plus straight b end fraction equals 1 over straight c fraction numerator straight x plus straight b plus straight x plus straight a over denominator open parentheses straight x plus straight a close parentheses begin display style open parentheses straight x plus straight b close parentheses end style end fraction equals 1 over straight c straight c left parenthesis 2 straight x plus straight b plus straight a right parenthesis equals open parentheses straight x plus straight a close parentheses open parentheses straight x plus straight b close parentheses straight x squared plus left parenthesis straight a plus straight b right parenthesis straight x plus ab equals 2 cx plus bc plus ac straight x squared plus left parenthesis straight a plus straight b minus 2 straight c right parenthesis straight x plus ab minus bc minus ac equals 0 Let space straight alpha space and space straight beta space be space the space two space roots space of space the space quadratic space equation. straight alpha space plus space straight beta equals negative left parenthesis straight a plus straight b minus 2 straight c right parenthesis equals 2 straight c minus straight a minus straight b αβ equals ab minus bc minus ac According space to space the space question comma straight alpha equals negative straight beta rightwards double arrow straight alpha space plus space straight beta equals 0 rightwards double arrow 2 straight c minus straight a minus straight b equals 0 rightwards double arrow 2 straight c equals straight a plus straight b rightwards double arrow straight c equals fraction numerator straight a plus straight b over denominator 2 end fraction end style
Answered by Sneha shidid | 20 Nov, 2018, 11:42: AM

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CBSE 11-science - Maths
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