Question

If a and b are integers of the polynomial f (x) = x² + x + 1, find the value of 1 / a² + 1 / b².​

Answer 1

Answer:

$- 1$

Step-by-step explanation:

$a + b = - 1 \\ \\ ab = 1 \\ \\ therefore \: \: \frac{1}{ {a}^{2} } + \frac{1}{ {b}^{2} } = \frac{ {a}^{2} + {b}^{2} }{( {ab)}^{2} } \\ \\ = \frac{{(a + b)}^{2} - 2ab}{( {ab)}^{2} } \\ \\ = \frac{ {( - 1)}^{2} - 2(1)}{ {(1)}^{2} } \\ \\ = \frac{1 - 2}{1} \\ \\ = - 1$