Question

tìm gt của bt
6xy(xy-y^2)-8x^2(x-y)^2+5y(x^2-xy), tại x=1/2;y=2

Answer 1

\(A=6xy\left(xy-y^2\right)-8x^2\left(x-y\right)^2+5y\left(x^2-xy\right)\)

\(=6xy^2\left(x-y\right)-8x^2\left(x-y\right)\left(x-y\right)+5xy\left(x-y\right)\)

\(=x\left(x-y\right)\left(6y^2-8x\left(x-y\right)+5y\right)\)

\(=x\left(x-y\right)\left(6y^2-8x^2+8xy+5y\right)\)

\(=x\left(x-y\right)\left[2\left(3y+2x\right)\left(y-2x\right)+16xy+5y\right]\)

Thay x=1/2; y =2 ta được

\(A=\frac{1}{2}\left(\frac{1}{2}-2\right)\left[0+16\cdot\frac{1}{2}\cdot2+5\cdot2\right]=-\frac{1}{2}\cdot\frac{3}{2}\cdot26=-\frac{39}{2}\).

Answer 2

6xy ( xy - y² ) - 8x² ( x - y )² + 5y ( x² - xy ) 

= 6x²y² - 6xy³ - 8x³ + 8x²y + 5yx² - 5xy²

= xy ( 6xy - 6y² + 8x + 5x - 5y ) - 8x³

Thay x= \(\frac{1}{2}\)     ; y = 2

= 6 - 6.4 + 8. \(\frac{1}{2}\)      + 5. \(\frac{1}{2}\)       -  5.2 - 8.8

=> 6 - 24 + 4 + 2,5 - 10 - 64

= - 85,5

Answer 3

\(6xy\left(xy-ỳ^2\right)-8x^2\left(x-y\right)^2+5y\left(x^2-xy\right)\)

\(=6x^2y^2-6xy^3-8x^2\cdot\left(x^2-y^2\right)+5x^2y-5xy^2\)

\(=6x^2y^2-6xy^3-8x^4+8x^2y^2+5x^2y-5xy^2\)

\(=-8x^4+14x^2y^2+5x^2y-6xy^3-5xy^2\)

 Thay \(x=\frac{1}{2};y=2\) vào đa thức \(-8x^4+14x^2y^2+5x^2y-6xy^3-5xy^2\)

\(-8\left(\frac{1}{2}\right)^4+14\left(\frac{1}{2}\right)^2\cdot2^2+5\left(\frac{1}{2}\right)^2\cdot2-6\cdot\frac{1}{2}\cdot2^3-5\cdot\frac{1}{2}\cdot2^2\)

\(=-\frac{1}{2}+14+\frac{5}{2}-24-10\)

\(=-18\)