The sum of two numbers is 15 and the sum of their squares is 113. Find the numbers. · ABC26GN1637
Subject: General Aptitude · Chapter: Problems on Numbers · Exam: R.R.B. 2006
The sum of two numbers is 15 and the sum of their squares is 113. Find the numbers.
Answer
No answer key was printed for this question.
Explanation
Let the numbers be $x$ and $(15-x)$. Then, $x^{2}+(15-x)^{2}=113 \Rightarrow x^{2}+225+x^{2}-30x=113 \Rightarrow 2x^{2}-30x+112=0 \Rightarrow x^{2}-15x+56=0 \Rightarrow (x-7)(x-8)=0 \Rightarrow x=7 \text{ or } x=8$. So, the numbers are 7 and 8.
Explanation as extracted from the printed page; notation may be imperfect.