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Rashmi Bajpayee 2 years, 12 months ago

Let the three consecutive natural numbers be x, x + 1 and x + 2.

Then, According to question,

{tex}{\left( {x + 1} \right)^2} = {\left( {x + 2} \right)^2} - {x^2} + 60{/tex}

=> {tex}{x^2} + 2x + 1 = {x^2} + 4x + 4 - {x^2} + 60{/tex}

=> {tex}{x^2} - 2x - 63 = 0{/tex}

=> {tex}{x^2} - 9x + 7x - 63 = 0{/tex}

=> {tex}x(x-9)+7(x-9)=0{/tex}

=> {tex}(x-9)(x+7)=0{/tex}

=> {tex}x=9{/tex} and {tex}x=-7{/tex} (neglected, as it is not a natural number)

Therefore, the three consecutive natural numbers are 9, 10 and 11.

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