If x is added to each of numbers 3, 9, 21 so | vedclass

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Question

(a) $3 + x,\;9 + x,\;21 + x$ are in $G.P.$

$ \Rightarrow $ ${(9 + x)^2} = (3 + x)(21 + x)$

$ \Rightarrow $ $81 + {x^2} + 18x = {x^2} + 24x + 63$

Vedclass · Accepted Answer

$3$

Vedclass · Answer

(a) $3 + x,\;9 + x,\;21 + x$ are in $G.P.$

$ \Rightarrow $ ${(9 + x)^2} = (3 + x)(21 + x)$

$ \Rightarrow $ $81 + {x^2} + 18x = {x^2} + 24x + 63$

$ \Rightarrow $ $6x = 18$ or $x = 3$.

Trick : Check for $(a)$, $3 + 3,\;9 + 3,\;21 + 3$ are in $G.P.$

If $x$ is added to each of numbers $3, 9, 21$ so that the resulting numbers may be in $G.P.$, then the value of $x$ will be

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