cho f(x)=ax^3+bx^2+cx+d, trong đó a,b,c,d là hằng số thoả mãn: b=3a+c.Chưng stor rằng: f(1)=f(-2) 01/08/2021 Bởi Reese cho f(x)=ax^3+bx^2+cx+d, trong đó a,b,c,d là hằng số thoả mãn: b=3a+c.Chưng stor rằng: f(1)=f(-2)
\( f(1)=a.1^3+b.1^2+c.1+d=a+b+c+d\) mà \(b=3a+c\) \(→f(1)=a+3a+c+c+d=4a+2c+d(1)\) \(f(-2)=a.(-2)^3+b.(-2)^2+c.(-2)+d=-8a+4b-2c+d\) mà \(b=3a+c\) \(→f(-2)=-8a+4(3a+c)-2c+d=-8a+12a+4c-2c+d=4a+2c+d(2)\) Từ (1)(2) \(→f(1)=f(-2)\) khi \(b=3a+c\) Bình luận
`f(x)=ax^3+bx^2+cx+d` `b=3a+c` `⇒f(x)=ax^3+(3a+c)x^2+cx+d` `f(1)=a.1^3+3a+c.1^2+c.1+d` `⇒f(1)=a+3a+c+c+d` `=4a+2c+d` `f(-2) = a.(-2)^3 + (3a + c).(-2)^2+c.(-2)+d` `⇒f(-2)=a.(-8) + 12a + 4c – 2c +d `=4a + 2c + d` `⇒f(1)=f(-2)` Bình luận
\( f(1)=a.1^3+b.1^2+c.1+d=a+b+c+d\)
mà \(b=3a+c\)
\(→f(1)=a+3a+c+c+d=4a+2c+d(1)\)
\(f(-2)=a.(-2)^3+b.(-2)^2+c.(-2)+d=-8a+4b-2c+d\)
mà \(b=3a+c\)
\(→f(-2)=-8a+4(3a+c)-2c+d=-8a+12a+4c-2c+d=4a+2c+d(2)\)
Từ (1)(2) \(→f(1)=f(-2)\) khi \(b=3a+c\)
`f(x)=ax^3+bx^2+cx+d`
`b=3a+c`
`⇒f(x)=ax^3+(3a+c)x^2+cx+d`
`f(1)=a.1^3+3a+c.1^2+c.1+d`
`⇒f(1)=a+3a+c+c+d`
`=4a+2c+d`
`f(-2) = a.(-2)^3 + (3a + c).(-2)^2+c.(-2)+d`
`⇒f(-2)=a.(-8) + 12a + 4c – 2c +d
`=4a + 2c + d`
`⇒f(1)=f(-2)`