Answer:
Let the three consecutive natural numbers be \[x,x+1\] and \[x+2\]. According to the given condition, \[\therefore {{(x+1)}^{2}}-[{{(x+2)}^{2}}-{{x}^{2}}]=60\] \[{{x}^{2}}+1+2x-[(x+2-x)(x+2+x)]=60\] \[{{x}^{2}}+2x+1-[2(2+2x)]=60\] \[{{x}^{2}}+2x+1-4-4x=60\] \[{{x}^{2}}-2x-63=0\] \[{{x}^{2}}-9x+7x-63=0\] \[x(x-9)+7(x-9)=0\] \[(x+7)(x-9)=0\] \[\therefore x=9\] or \[-7\] \[\therefore x=9\] (neglect \[x=-7\]) \[\therefore \] Number are 9, 10, 11.
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