已知:x^2+x=1/3,求6x^4+15x^3+10x^2的值1)已知:x^2+x=1/3,求6x^4+15x^3+10x^2的值2)若(y^2+my+4)(y^2-2y+n)的乘积中不含y^2与y^3项,求m,n的值
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![已知:x^2+x=1/3,求6x^4+15x^3+10x^2的值1)已知:x^2+x=1/3,求6x^4+15x^3+10x^2的值2)若(y^2+my+4)(y^2-2y+n)的乘积中不含y^2与y^3项,求m,n的值](/uploads/image/z/5183695-55-5.jpg?t=%E5%B7%B2%E7%9F%A5%3Ax%5E2%2Bx%3D1%2F3%2C%E6%B1%826x%5E4%2B15x%5E3%2B10x%5E2%E7%9A%84%E5%80%BC1%EF%BC%89%E5%B7%B2%E7%9F%A5%3Ax%5E2%2Bx%3D1%2F3%2C%E6%B1%826x%5E4%2B15x%5E3%2B10x%5E2%E7%9A%84%E5%80%BC2%EF%BC%89%E8%8B%A5%EF%BC%88y%5E2%2Bmy%2B4%29%28y%5E2-2y%2Bn%29%E7%9A%84%E4%B9%98%E7%A7%AF%E4%B8%AD%E4%B8%8D%E5%90%ABy%5E2%E4%B8%8Ey%5E3%E9%A1%B9%2C%E6%B1%82m%2Cn%E7%9A%84%E5%80%BC)
已知:x^2+x=1/3,求6x^4+15x^3+10x^2的值1)已知:x^2+x=1/3,求6x^4+15x^3+10x^2的值2)若(y^2+my+4)(y^2-2y+n)的乘积中不含y^2与y^3项,求m,n的值
已知:x^2+x=1/3,求6x^4+15x^3+10x^2的值
1)已知:x^2+x=1/3,求6x^4+15x^3+10x^2的值
2)若(y^2+my+4)(y^2-2y+n)的乘积中不含y^2与y^3项,求m,n的值
已知:x^2+x=1/3,求6x^4+15x^3+10x^2的值1)已知:x^2+x=1/3,求6x^4+15x^3+10x^2的值2)若(y^2+my+4)(y^2-2y+n)的乘积中不含y^2与y^3项,求m,n的值
(1)x²+x=1/3
6x⁴+15x³+10x²
= 6x²(x²+x)+9x(x²+x)+x²
=2x²+3x+x²
=3(x²+x)
=1
(2)
(y²+my+4)(y²-2y+n)
=y⁴ - 2y³ + ny² +my³ - 2my² + mny + 4y² - 8y+4n
=y⁴ +(m-2)y³ +(n-2m+4)y² +(mn-8)y +4n
因为不含y的2次方与y的3次方项,所以
m-2=0 ; n-2m+4=0
解得:m=2,n=2m-4=0