Question

$4x^{2} - 2x + 5$

$11x^{2} + 110x + 14$
помогите выделить квадраты! ​

Answer 1

Ответ:

$4 {x}^{2} - 2x + 5 = \\ = {(2x)}^{2} - 2 \times 2x \times \frac{1}{2} + \frac{1}{4} + \frac{19}{4} = \\ = {(2x - \frac{1}{2}) }^{2} + \frac{19}{4}$

$11 {x}^{2} + 110x + 14 = \\ = {( \sqrt{11} x)}^{2} + 2 \times \sqrt{11} x \times \frac{55}{ \sqrt{11} } + \frac{ {55}^{2} }{11} + (14 - \frac{ {55}^{2} }{11} ) = \\ = {( \sqrt{11} x + \frac{55}{ \sqrt{11} }) }^{2} + \frac{154 - 3025}{11} = \\ = {( \sqrt{11} x + \frac{55}{ \sqrt{11} } )}^{2} - 261$