Question

tìm x biết : 
a, (x+1)²+2x(x-2)=3(x+4)(x+1)

chứng minh rằng biểu thức luôn dương với mọi giá trị của x

M=x²+12x+50

Answer 1

\(a,\left(x+1\right)^2+2x\left(x-2\right)=3\left(x+4\right)\left(x+1\right)\)

\(x^2+2x+1+2x^2-4x=3\left(x^2+5x+4\right)\)

\(3x^2-2x+1=3x^2+15x+12\)

\(\Rightarrow3x^2-2x+1-3x^2-15x-12=0\)

\(\Rightarrow-17x=11\)

\(\Rightarrow x=-\frac{11}{17}\)

\(b,M=x^2+12x+50\)

\(M=x^2+2.6.x+6^2+14\)

\(M=\left(x+6\right)^2+14\ge14>0\)

=> M luôn dương 

Answer 2

\(\left(x+1\right)^2+2x\left(x-2\right)=3\left(x+4\right)\left(x+1\right).\)

\(\Leftrightarrow x^2+2x+1+2x^2-4x=3.(x^2+x+4x+4)\)

\(\Leftrightarrow x^2-2x+2x^2+1=3x^2+15x+12\)

\(\left(x^2-3x^2+2x^2\right)=\left(15x+2x\right)+12-1\)

\(17x+11=0\)

\(\Leftrightarrow x=\frac{-11}{17}\)