Question

Bài 1 : C/m các biểu thức sau không phụ thuộc vào x :

a,(x+1)^3-(x-1)^3-6(x+1)(x-1)

b, (x+5)^2+(x-5)^2/x^2+25

c,(2x+5)^2+(5x-2)^2/x^2+1

Answer 1

a/(x+1)³-(x-1)³-6(x+1)(x-1)

=(x³+3x²+3x+1)-(x³-3x²+3x-1)-6(x²-1)

=x³+3x²+3x+1-x³+3x²-3x+1-6x²+6

=8(không phụ vào x)

Answer 2

a: \(\left(x+1\right)^3-\left(x-1\right)^3-6\left(x+1\right)\left(x-1\right)\)

\(=x^3+3x^2+3x+1-\left(x^3-3x^2+3x-1\right)-6\left(x^2-1\right)\)

\(=x^3+3x^2+3x+1-x^3+3x^2-3x+1-6x^2+6\)

=8

b: \(\dfrac{\left(x+5\right)^2+\left(x-5\right)^2}{x^2+25}\)

\(=\dfrac{x^2+10x+25+x^2-10x+25}{x^2+25}\)

\(=\dfrac{2x^2+50}{x^2+25}=2\)

c: \(\dfrac{\left(2x+5\right)^2+\left(5x-2\right)^2}{x^2+1}\)

\(=\dfrac{4x^2+20x+25+25x^2-20x+4}{x^2+1}\)

\(=\dfrac{29x^2+29}{x^2+1}=29\)