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Question Number 215137 by hardmath last updated on 29/Dec/24

$$\mathrm{If}\overline{\mathrm{ab}}+\overline{\mathrm{ba}}={\mathrm{n}}^2$$$$\mathrm{Find}\max (\mathrm{a}\cdot \mathrm{b})-\min (\mathrm{a}\cdot \mathrm{b})=?$$

Answered by mahdipoor last updated on 29/Dec/24

$$ab+ba=11(a+b)={11}^2=n^2\Rightarrow 11=a+b\Rightarrow$$$$max(a.b)=30,min(a.b)=18\Rightarrow 30-18=12$$

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