Question

Cum se descompune?? Va rog dau coroana, urgent!!!!!!!!!

Answer 1

${x}^{2} - 4xy - {y}^{2} = \\ \\ a(x - \frac{ - b + \sqrt{ {b}^{2} - 4ac } }{2a})(x - \frac{ - b - \sqrt{ {b}^{2} - 4ac } }{2a} \\ \\ (x - \frac{4y + \sqrt{( - 4y) ^{2} - 4 \times - {y}^{2} } }{2})(x - \frac{4y - \sqrt{( - 4y) ^{2} - 4 \times - {y}^{2} } }{2} \\ \\ (x - \frac{4y + 2\sqrt{5} y}{2})(x - \frac{4y - 2 \sqrt{5} y}{2}) \\ \\ (x - \frac{2y(2 + \sqrt{5}) }{2})(x - \frac{4y - 2 \sqrt{5} y}{2}) \\ \\ (x - (2 + \sqrt{5})y)(x - \frac{4y - 2 \sqrt{5} y}{2}) \\ \\ (x - (2 + \sqrt{5})y)(x - \frac{2(2 - \sqrt{5}) }{2} \\ \\ (x - (2 + \sqrt{5})y)(x - \frac{2(2 - \sqrt{5} y)}{2} \\ \\ (x - (2 + \sqrt{5})y)(x - (2 - \sqrt{5})y)$

Answer 2

x² -4xy - y² = x² - 4xy +4y² - 5y² =

= (x - 2y)² - 5y² = (x-2y)² - (√5 y)² =

= [(x-2y) + √5 y]·[(x-2y) - √5 y] =

=[ x - (2 -√5)y]·[x - (2 +√5)y]