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KyleSpencer
@KyleSpencer
July 2022
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найдите произведение аб если а^3-b^3= -37 и a-b= -1
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AnonimusPro
Verified answer
A^3-b^3=(a-b)(a^2+ab+b^2)
a-b=-1 и a^3-b^3=37
поэтому:
-(a^2+ab+b^2)=-37
a^2+ab+b^2=37
выражаем a:
a=b-1
подставим:
(b-1)^2+b(b-1)+b^2=37
b^2-2b+1+b^2-b+b^2-37=0
3b^2-3b-36=0
b^2-b-12=0
D=1+48=49=7^2
b1=(1+7)/2=4
b2=-6/2=-3
a1=4-1=3
a2=-3-1=-4
произведение:
4*3=12
(-3)*(-4)=12
Ответ: 12
4 votes
Thanks 5
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Answers & Comments
Verified answer
A^3-b^3=(a-b)(a^2+ab+b^2)a-b=-1 и a^3-b^3=37
поэтому:
-(a^2+ab+b^2)=-37
a^2+ab+b^2=37
выражаем a:
a=b-1
подставим:
(b-1)^2+b(b-1)+b^2=37
b^2-2b+1+b^2-b+b^2-37=0
3b^2-3b-36=0
b^2-b-12=0
D=1+48=49=7^2
b1=(1+7)/2=4
b2=-6/2=-3
a1=4-1=3
a2=-3-1=-4
произведение:
4*3=12
(-3)*(-4)=12
Ответ: 12