Question

Cho x - y = 7. Tính giá trị của biểu thức:

B= x(x + 2) + y(y - 2) - 2xy + 37

Answer 1

Ta có

\(B=x^2+2x+y^2-2y-2xy+38\)

\(\Rightarrow B=\left(x^2-2xy+y^2\right)+\left(2x-2y\right)+37\)

\(\Rightarrow B=\left(x-y\right)^2-2\left(x-y\right)+37\)

\(\Rightarrow B=7^2-2.7+37\)

\(\Rightarrow B=49-14+37\)

\(\Rightarrow B=72\)

Answer 2

\(B=x\left(x+2\right)+y\left(y-2\right)-2xy+37\)

\(=x^2+2x+y^2-2y-2xy+37\)

\(=\left(x^2+y^2-2xy+1+2x-2y\right)+36\)

\(=\left(x-y+1\right)^2+36\)

\(=\left(7+1\right)^2+36\)

\(=64+36\)

\(=100\)