Q.If \(\sum\limits_{i=1}^5 x_i = 5\) and \(\sum\limits_{i=1}^5 x_i^2 = 14\), then the value of \(\sum\limits_{i=1}^5 2x_i(x_i - 3)\) will be — (a) 2 (b) -2 (c) 0 (d) 4
Answer: B
\(\sum \limits_{i=1}^5 2x_i(x_i - 3)\) \(= \sum \limits_{i=1}^5 2x_i^2 - \sum \limits_{i=1}^5 6x_i\) \(= 2 \times \sum \limits_{i=1}^5 x_i^2 - 6 \times \sum \limits_{i=1}^5 x_i\) \(= 2 \times 14 - 6 \times 5\) \(= 28 - 30\) \(= -2\)
Similar Questions