Please solve question no. 13....

Dear Student,

Please find below the solution to the asked query:

$$\begin{gathered} \mathrm{Let} \mathrm{the} \mathrm{three} \mathrm{consecutive} \mathrm{natural} \mathrm{numbers} \mathrm{are} \\ \mathrm{x}, \mathrm{x} + 1 \mathrm{and} \mathrm{x} + 2 \\ \mathrm{then} \mathrm{according} \mathrm{to} \mathrm{question} \\ {\left(\mathrm{x} + 1\right)}^2 = {\left(\mathrm{x} + 2\right)}^2 - {\mathrm{x}}^2 + 60 \\ \Rightarrow {\mathrm{x}}^2 + 2\mathrm{x} + 1 = {\mathrm{x}}^2 + 4\mathrm{x} + 4 - {\mathrm{x}}^2 + 60 \\ \Rightarrow {\mathrm{x}}^2 + 2\mathrm{x} + 1 = 4\mathrm{x} + 64 \\ \Rightarrow {\mathrm{x}}^2 + 2\mathrm{x} + 1 - 4\mathrm{x} - 64 = 0 \\ \Rightarrow {\mathrm{x}}^2 - 2\mathrm{x} - 63 = 0 \\ \Rightarrow {\mathrm{x}}^2 - 9\mathrm{x} + 7\mathrm{x} - 63 = 0 \\ \Rightarrow \mathrm{x} \left(\mathrm{x} - 9\right) + 7 \left(\mathrm{x} - 9\right) = 0 \\ \Rightarrow \left(\mathrm{x} - 9\right) \left(\mathrm{x} + 7\right) = 0 \\ \Rightarrow \mathrm{x} - 9 = 0 \mathrm{or} \mathrm{x} + 7 = 0 \\ \Rightarrow \mathrm{x} = 9 \mathrm{or} \mathrm{x} = -7 \\ \mathrm{But} \mathrm{x} = -7 \mathrm{is} \mathrm{rejected} \mathrm{as} \mathrm{it} \mathrm{is} \mathrm{not} \mathrm{natural} \mathrm{number} \\ \therefore \mathrm{x} = 9 \\ \mathrm{then} \mathrm{the} \mathrm{three} \mathrm{consecutive} \mathrm{natural} \mathrm{numbers} \mathrm{are} 9, 10 \mathrm{and} 11. \end{gathered}$$



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