ABC26GN1724 · Problems on Numbers
Subject: General Aptitude · Chapter: Problems on Numbers · Exam: · Marks: · Difficulty:
The sum of the squares of three consecutive natural numbers is 2030 . What is the middle number?
Answer
Explanation
Let the numbers be $x, x+1$ and $x+2$. Then, $x^{2}+(x+1)^{2}+(x+2)^{2}=2030$ $$\begin{aligned} & \Leftrightarrow 3 x^{2}+6 x-2025=0 \\ & \Leftrightarrow x^{2}+2 x-675=0 \\ & \Leftrightarrow(x+27)(x-25)=0 \\ & \Leftrightarrow x=25 . \end{aligned}$$
Explanation as extracted from the printed page; notation may be imperfect.
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