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InterviewSolution
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If x,y,z be three positive prime numbers. The progression in which `sqrt(x),sqrt(y),sqrt(z)` can be three terms (not necessarily consecutive) isA. APB. GPC. HPD. None of these |
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Answer» Correct Answer - D `:.a,b,c` are positive prime numbers. Let `sqrt(a),sqrt(b),sqrt(c)` are 3 terms of AP. [not necessarily consecutive ] Then, `sqrt(a)=A+(p-1)D " " "....(i)"` `sqrt(b)=A+(q-1)D " " "....(ii)"` `sqrt(c)=A+(r-1)D " " "....(iii)"` [A and D be the first term and common difference of AP] `sqrt(a)-sqrt(b)=(p-q)D " " "....(iv)"` `sqrt(b)-sqrt(c )=(q-r)D " " "....(v)"` `sqrt(c)-sqrt(a)=(r-p)D " " "....(vi)"` On dividing Eq.(v), we get `(sqrt(a)-sqrt(b))/(sqrt(b)-sqrt(c))=(p-q)/(q-r)" " "....(vii)"` Since,p,q,r are natural numbers and a,b,c are positive prime numbers, so Eq. (vii) does not hold. So, `sqrt(a),sqrt(b),sqrt(c)` cannot be the 3 terms of AP. [not necessarily consecutive ] Similarly, we can show that `sqrt(a),sqrt(b),sqrt(c)` cannot be any 3 terms of GP andHP. [ not necessarily, consecutive]. |
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