Question

Proste zadanka.

1. Zapisz w prostszej postaci.
a) (x-1)² + (x+2)² + (x-3) * (x+3)
b) (2a+3)² - (a+2) * (2-a) - (3a-2)²
c) (b√2+1)² - (1-b√2-3) * (b√2+3)
d) 3(a-2b)² + 6(a+b)² - 9(a-√6) * (a+√6)

2. Sprawdź, czy (√2+1)² * (√2+1) = 7+5√2

3. Sprawdź, czy (5-√5)² = (√5-5)²

Answer 1

A)
(x-1)*(x-1)+(x+2)*(x+2)+(x-3)*(x+3)=x²-x-x+1+x²+2x+2x+4+x²+3x-3x-9=3x²-2x-4+4x=3x²+2x-4

b)
(2a+3)*(2a+3)-(a+2)*(2-a)-(3a-2)*(3a-2)=4a²+6a+6a+9-2a-a²+4-2a-9a²-6a-6a+4=-4a+17

c)
(b√2+1)*(b√2+1)-(1-b√2-3)*(b√2+3)=b²√2²+b√2+b√2+1-b√2+3-b²√2²-3b√2-3b√2-9=2b²+b√2+b√2+1-b√2+3-2b²-3b√2-3b√2-9=-5b√2-8

d)
3*(a-2b)*(a-2b)+6*(a=b)*(a+b)-9(a-√6)*(a+√6)=3*(a²-2ab)-2ab+4b²+6*(a²+ab+ab+b²)-9*(a²+√6a-√6a-√6²)=3a²-6ab-2ab+4b²+6a²+6ab+6ab+6b²-9a²+9√6a-9√6a-6=4ab+10b²-6


Nie wiem czy to będzie dobrze.