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If `2010` is a root of `x^(2)(1 - pq) - x(p^(2) + q^(2)) - (1 + pq) = 0` and `2010` harmonic mean are inserted between `p` and `q` then the value of `(h_(1) - h_(2010))/(pq(p - q))` is |
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Answer» Correct Answer - 1 Let `2010 = n` `:. n^(2)(1-pq)-n(p^(2)-q^(2))-(1+pq) = 0` `(n^(2)-1)=pq(n^(2)+1)+n(p^(2)-q^(2))….(1)` `d=(p-q)/(pq(n+1)):.(1)/(h_(1))=(1)/(p)+d,(1)/(h_(2))=(1)/(q)-d` `h_(1)-h_(n)=(1)/((1)/(p)+d)-(1)/((1)/(q)-d)=(P)/(1+pd)-(q)/(1-qd)` `(p)/(1+(p(p-q))/(pq(n+1)))-(q)/(1+(q(p-q))/(pq(n+1)))` `= (pq(p-q)(n^(2)-1))/((qn+p)(pn+q))` `=(pq(p-q)[pq(n^(2)+1)+n(p^(2)+q^(2))])/((qn+p)(pn+q))` `:. (h_(1) - h_(n))/(pq(p-q)) = 1` |
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