Question

Doprowadź wyrażenie do najprostszej postaci:
[tex]x = \sqrt{7} - 2\sqrt{5}[/tex]
[tex]y = 3 - \sqrt{5}[/tex]
[tex]W = ( y - 2x)^{2} - (2y + x) * (x - 2y) - ( 3y - 2x)^{2} - 4xy =[/tex]

Answer 1

Odpowiedź:

x = √7 - 2√5

y = 3 - √5

W(x) = (y - 2x)² - (2y + x)(x - 2y) - (3y - 2x)² - 4xy =

= y² - 4xy - (2xy + x² - 4y² - 2xy) - ( 9y² - 12xy + 4x²) - 4xy =

= y² - 4xy - 2xy - x² - 4y² + 2xy - 9y² + 12xy - 4x² - 4xy =

= - 12y² - 5x² + 4xy = - 5x² - 12y² + 4xy =

= - 5(√7 - 2√5)² - 12(3 - √5)² + 4(√7 - 2√5)(3 - √5) =

= - 5(7 - 4√(7 * 5) + 4 * 5) - 12(9 - 6√5 + 5) + 4(3√7 - 6√5 - √(7 * 5) +

+ 2√5² = - 5(7 - 4√35 + 20) - 12(14 - 6√5) + 4(3√7 - 6√5 - √35) =

= - 5(27 - 4√35) - 168 + 72√5 + 12√7 - 24√5 - 4√35 =

= - 135 + 20√35 - 168 + 72√5 + 12√7 - 24√5 - 4√35 =

= - 303 + 48√5 + 12√7 + 16√35