InterviewSolution
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InterviewSolution
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If `a ,b ,c ,da n dp`are distinct real numbers such that `(a^2+b^2+c^2)p^2-2(a b+b c+c d)p+(b^2+c^2+d^2)lt=0,`then prove that `a ,b ,c , d`are in G.P.A. are in APB. are in GPC. are in HPD. satisfy `ab = cd` |
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Answer» Correct Answer - B Here, `(a^(2) + b^(2) + c^(2)) p^(2) -2 (ab + bc + cd) p + (b^(2) + c^(2) + d^(2)) le 0` `rArr (a^(2) p^(2) - 2abp + b^(2)) + (b^(2) p^(2) -2bcp + c^(2)) + (c^(2) p^(2) -2cdp + d^(2)) le 0` `rArr (ap - b)^(2) + (bp -c)^(2) + (cp -d)^(2) le 0` [since, sum of squares is never less than zero] Since, each of the squares is zero. `:. (ap = b)^(2) = (bp -c)^(2) + (cp -d)^(2) = 0` `rArr p = (b)/(a) = (c)/(b) = (d)/(c)` `:.` a, b, c, d are in GP. |
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