{"id":"informator-maturalny-matematyka-2010/zad/59","paper_id":"informator-maturalny-matematyka-2010","number":"59","points":2,"ptype":"open","subject":"matematyka","category":"informator-maturalny","year":2010,"month":null,"level":null,"text":"Zadanie 59. (2 pkt)\nWielomiany\n( )\n(\n)\n2\nb\nx\nax\nx\nW\ni ( )\nx\nx\nx\nx\nV\n2\n3\n2\nsą równe. Oblicz\ni .\na\nb","answer":null,"answer_text":null,"solution":"W(x)=ax(x+b)^2 = ax(x^2+2bx+b^2) = ax^3+2abx^2+ab^2x.\nPorównując z V(x)=x^3+2x^2+x: a=1, 2ab=2, ab^2=1.\nZ a=1: 2b=2 → b=1. Sprawdzenie: ab^2=1*1=1 ✓.\nOdpowiedź: a=1, b=1.","image":"img/informator-maturalny-matematyka-2010/zad-59.webp","solution_image":null,"topics":null,"page_from":84,"source":"ai","answer_source":null,"answer_text_source":null,"solution_source":"ai","text_source":"ocr","source_label":"Matematyka · Informator maturalny · 2010","subject_label":"Matematyka","category_label":"Informator maturalny","text_html":"

Zadanie 59. (2 pkt)
Wielomiany
( )
(
)
2
b
x
ax
x
W
i ( )
x
x
x
x
V
2
3
2
są równe. Oblicz
i .
a
b

","solutions":[{"source":"ai","label":"AI","kind":"text","html":"

W(x)=ax(x+b)^2 = ax(x^2+2bx+b^2) = ax^3+2abx^2+ab^2x.
Porównując z V(x)=x^3+2x^2+x: a=1, 2ab=2, ab^2=1.
Z a=1: 2b=2 → b=1. Sprawdzenie: ab^2=1*1=1 ✓.
Odpowiedź: a=1, b=1.

"}]}