Odpowiedź :
(√5+x)²-(√5-x)²+(x+√5)(√5-x) =
=5+2√5+x²-(5-2√5+x²)+(√5+x)(√5-x)=
=5+2√5+x²-5+2√5-x²+5-x²=
=5-x²+4√5
5-x²+4√5=5-(√5-1)²+4√5=5-5+2√5-1=2√5-1
(3-x)²-(x+1/3)²+2/9=
9-6x+x²-x²-2/3x-1/9+2/9=
9-1/9-6 i 2/3x=
8 i 8/9 -6 i 2/3x
:)
=5+2√5+x²-(5-2√5+x²)+(√5+x)(√5-x)=
=5+2√5+x²-5+2√5-x²+5-x²=
=5-x²+4√5
5-x²+4√5=5-(√5-1)²+4√5=5-5+2√5-1=2√5-1
(3-x)²-(x+1/3)²+2/9=
9-6x+x²-x²-2/3x-1/9+2/9=
9-1/9-6 i 2/3x=
8 i 8/9 -6 i 2/3x
:)
rozwiąż równanie:
(3-x)²-(x+1/3)²+2/9
9 - 6x + x² - (x²+ ²/6x + 1/9) +²/9 =
= 9 - 6x + x² - x² - ²/6x - 1/9 + 2/9 =
= 6 i 1/3 x + 9 i 1/9
(3-x)²-(x+1/3)²+2/9
9 - 6x + x² - (x²+ ²/6x + 1/9) +²/9 =
= 9 - 6x + x² - x² - ²/6x - 1/9 + 2/9 =
= 6 i 1/3 x + 9 i 1/9