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Question Number 192444 by Mastermind last updated on 18/May/23

$$\mathrm{The}\mathrm{sum}\mathrm{of}\mathrm{three}\mathrm{numbers}\mathrm{in}\mathrm{arith}-$$$$\mathrm{metic}\mathrm{progression}\mathrm{is}18\mathrm{and}\mathrm{sum}\mathrm{of}$$$$\mathrm{square}\mathrm{is}206.\mathrm{find}\mathrm{the}\mathrm{numbers}$$

Commented by Tinku Tara last updated on 19/May/23

$$\mathrm{Automatic}\mathrm{tagging}\mathrm{may}\mathrm{sometime}$$$$\mathrm{tag}\mathrm{wrong}\mathrm{question}.$$$$\mathrm{will}\mathrm{fix}\mathrm{this}\mathrm{in}\mathrm{future}\mathrm{updates}$$

Commented by Mastermind last updated on 18/May/23

$$\mathrm{the}\mathrm{answer}\mathrm{you}\mathrm{tag}\mathrm{is}\mathrm{already}\mathrm{deleted}$$$$\mathrm{from}\mathrm{forum}$$

Commented by Frix last updated on 19/May/23

$$\mathrm{It}\mathrm{can}\mathrm{be}\mathrm{triggered}\mathrm{like}\mathrm{this}:$$$$q=546213$$

Commented by Frix last updated on 19/May/23

$$...\mathrm{or}\mathrm{this}:$$$$\mathrm{Quod}\mathrm{erat}\mathrm{demonstrandum}x=567123$$

Answered by deleteduser1 last updated on 18/May/23

$$a-d+a+a+d=3a=18\Rightarrow a=6$$$${(6-d)}^2+6^2+{(6+d)}^2=108+2d^2=206\Rightarrow d=\underset{-}{+}7$$$$(-1,6,13);(13,6,-1)$$

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