Question
The sum of the squares of three consecutive natural numbers is 2030.What is the middle number?
The sum of the squares of three consecutive natural numbers is 2030.What is the middle number?
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Solution
The correct option is B 26
Let the numbers be x and x+1 and x+2
Then, x2+(x+1)2+(x+2)2=2030⇔3x2+6x−2025=0. ⇔x2+2x−675=0⇔(x+27)(x−25)=0⇔x=25.
∴ Middle number = (x+1)=26.
26
Let the numbers be x and x+1 and x+2
Then, x2+(x+1)2+(x+2)2=2030⇔3x2+6x−2025=0. ⇔x2+2x−675=0⇔(x+27)(x−25)=0⇔x=25.
∴ Middle number = (x+1)=26.
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