A) 25
B) 26
C) 27
D) 28
Correct Answer: A
Solution :
| Let the three consecutive natural numbers be x, \[x+1\] and \[x+2\] |
| According to question, |
| \[{{x}^{2}}+{{(x+1)}^{2}}+{{(x+2)}^{2}}=2030\] |
| \[\Rightarrow \]\[{{x}^{2}}+{{x}^{2}}+2x+1+{{x}^{2}}+4x+4=2030\] |
| \[\Rightarrow \] \[3{{x}^{2}}+6x+5=2030\] |
| \[\Rightarrow \] \[3{{x}^{2}}+6x-2025=0\] |
| \[\Rightarrow \] \[{{x}^{2}}+2x-675=0\] |
| \[\Rightarrow \] \[{{x}^{2}}+27x-25x-675=0\] |
| \[\Rightarrow \] \[x\,\,(x+27)-25\,\,(x+27)=0\] |
| \[\Rightarrow \] \[(x-25)-25\,\,(x+27)=0\] |
| \[\therefore \] \[x=25\] and \[-\,\,27\] |
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