Question

Let a,b,c be positive integers such that is an integer. If a,b,c are in geometric progression and a' + a -14 5) the arithmetic mean of a,b,c is b + 2, then the value of 4 * is (JEE(Advanced)-2014, 3] a +1 ADI CAL

JEE/Engineering Exams

Maths

Solution

160

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Let ( a, b, c b a, a r, a v^{2} ) aso ( _{1} frac{a+b+c}{3}=b+2 ) ( Rightarrow quad a+a r+a x^{2}=39 r+6 ) ( Rightarrow quad a r^{2}-2 a r+a=6 ) ( Rightarrow quad a(r+)^{2}=frac{6}{9} ) ( Rightarrow quad frac{6}{9} ) must ( b e ) a perfect oquare [ begin{aligned} &=(r+1)^{2} text { is be } end{aligned} ] 3) ( a=6 ). ( gamma-1=pm 1 ) ( r=0,2,0 ) (mat possible) ( therefore quad a^{2}+a-14 ) ( operatorname{ajv} e^{frac{36+6-14}{7}}=4 ) thes nating solved by am ition