InterviewSolution
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InterviewSolution
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If `a ,b, c ,d`are in G.P, then `(b-c)^2+(c-a)^2+(d-b)^2`is equal to`A. `(a-d)^(2)`B. `(ad)^(2)`C. `(a+d)^(2)`D. `(a//d)^(2)` |
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Answer» Correct Answer - A Let r be the common ratio of the G.P., a,b,c,d. Then, `b=ar,c=ar^(2) and d=ar^(3)` ltbrRgt `therefore(b-c)^(2)+(c-a)^(2)+(d-b)^(2)` `=(ar-ar^(2))^(2)+(ar^(2)-a)^(2)+(ar^(3)-ar)^(2)` `=a^(r )r^(2)(1-r)^(2)+a^(2)(r^(2)-1)^(2)+a^(2)r^(2)(r^(2)-1)^(2)` `=a^(2)(r^(6)-2r^(3)+1)` `=a^(2)(1-r^(3))^(2)` `=(a-ar^(3))^(2)` `=(a-d)^(2)` |
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