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The sum of the squares of three consecutive natural numbers is 149.Find the numbers. |
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Answer» Let three consecutive natural numbers be `x,(x+1)and(x+2)` respectively. According to given condition `x^(2)+(x+1)^(2)+(x+2)^(2)=149` `impliesx^(2)+(x^(2)+1+2x)+(x^(2)+4+4x)=149` `implies3x^(2)+6x+5=149` `implies3x^(2)+6x-144=0` `impliesx^(2)+2x-48=0` `impliesx^(2)+8x-6x-48=0` `impliesx(x+8)-6(x+8)=0` `implies(x+8)(x-6)=0` `impliesx=-8andx=6` `impliesx=6" "(x=-8"is not a natural number")` Hence, the required natural number are `6,(6+1),(6+2)=6,7,8` respectively. |
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