Question

cho biểu thức P=\(\left(x+2\right)^2-2\left(x+2\right)\left(x+8\right)+\left(x-8\right)^2\)

tính nhanh giá trị củ biểu thức P tại x=\(-5\dfrac{3}{4}\)

Answer 1

P=(x+2)²-2(x+2)(x+8)+(x+8)²-(x+8)²+(x-8)²

= (x+2-x-8)²-[(x+8)²-(x-8)²]

=(-6)²-(x+8-x+8)(x+8+x-8)=36-16.2x=36-32.x=36-32.\(-5\dfrac{3}{4}=220\)

Answer 2

\(P=\left[\left(x+2\right)-\left(x+8\right)\right]^2+\left(x-8\right)^2-\left(x+8\right)^2\)

\(P=36+\left[\left(x-8\right)-\left(x+8\right)\right]\left[\left(x-8\right)+\left(x+8\right)\right]\)

\(P=36+\left[16\right].\left[2x\right]\)

\(P=36+16.2.\left(\dfrac{-17}{4}\right)=2.18-\dfrac{17.8}{4}=\dfrac{8\left(18-17\right)}{4}=2\)

Answer 3

P=[(x+2)-(x+8)]^2 +[(x-8)-(x+8)]{(x-8)+(x+8)]

P =(-6)^2 +[-16.(2x) ]

\(P=36-32.\dfrac{-17}{4}=36+8.17=4\left(9+34\right)=4.43=172\)