Question

(1 + 2x)² - (1 - 2y)² - 4(x + y) dla x = √3 + √2 ; y = √3 - √2

Wynik ma wyjść 16√6

Answer 1

(1 + 2x)² - (1 - 2y)² - 4(x + y) = [(1 + 2x) - (1 - 2y)][(1 + 2x) + (1 - 2y)] - 4(x + y) = [1 + 2x - 1 + 2y][1 + 2x + 1 - 2y] - 4(x + y) = 2(x + y)* 2[x - y + 1] - 4(x + y) = 4(x + y)(x - y + 1 -1) = 4(x + y)(x - y)

4(x + y)(x - y) = 4(√3 + √2 + √3 - √2)(√3 + √2 - √3 + √2) = 4*2√3*2*√2 = 16√6

Answer 2

1+4x²+4x-(1+4y²-4y)-4x-4y= 1+4x²+4x-1-4y²+4y-4x-4y=4x²-4y²

4x²-4y²= 4(√3+√2)²- 4(√2-√3)²= 4(9+4+2√6)-4(4+9-2√6)= 36+16+8√6-16-36+8√6=16√6