Câu hỏi của khanh lam

Question

Giusp mình

Yen Nhi · Accepted Answer

Bài 8:a) $x^2-2x+1=25$$\Rightarrow\left(x-1\right)^2=25$$\Rightarrow\orbr{\begin{cases}\left(x-1\right)^2=5^2\\left(x-1\right)^2=\left(-5\right)^2\end{cases}}\Rightarrow\orbr{\begin{cases}x-1=5\x-1=-5\end{cases}}\Rightarrow\orbr{\begin{cases}x=6\x=-4\end{cases}}$b) $\left(5x+1\right)^2-\left(5x-3\right)\left(5x+3\right)=30$$\Rightarrow25x^2+10x+1-25x^2+9=30$$\Rightarrow10x+10=30$$\Rightarrow10x=20$$\Rightarrow x=2$c) $\left(x-1\right)\left(x^2+x+1\right)-x\left(x+2\right)\left(x-2\right)=5$$\Rightarrow x^3-1-x\left(x^2-4\right)=5$$\Rightarrow x^3-1-x^3+4x=5$$\Rightarrow4x=6$$\Rightarrow x=\frac{3}{2}$d) $\left(x-2\right)^3-\left(x-3\right)\left(x^2+3x+9\right)+6\left(x+1\right)^2=15$$\Rightarrow x^3-6x^2+12x-8-\left(x^3-27\right)+6\left(x^2+2x+1\right)=15$$\Rightarrow x^3-6x^2+12x-8-x^3+27+6x^2+12x+6=15$$\Rightarrow24x+25=15$$\Rightarrow24x=-10$$\Rightarrow x=\frac{-5}{12}$Câu trả lời: Bài 8:a) $x^2-2x+1=25$$\Rightarrow\left(x-1\right)^2=25$$\Rightarrow\orbr{\begin{cases}\left(x-1\right)^2=5^2\\left(x-1\right)^2=\left(-5\right)^2\end{cases}}\Rightarrow\orbr{\begin{cases}x-1=5\x-1=-5\end{cases}}\Rightarrow\orbr{\begin{cases}x=6\x=-4\end{cases}}$b) $\left(5x+1\right)^2-\left(5x-3\right)\left(5x+3\right)=30$$\Rightarrow25x^2+10x+1-25x^2+9=30$$\Rightarrow10x+10=30$$\Rightarrow10x=20$$\Rightarrow x=2$c) $\left(x-1\right)\left(x^2+x+1\right)-x\left(x+2\right)\left(x-2\right)=5$$\Rightarrow x^3-1-x\left(x^2-4\right)=5$$\Rightarrow x^3-1-x^3+4x=5$$\Rightarrow4x=6$$\Rightarrow x=\frac{3}{2}$d) $\left(x-2\right)^3-\left(x-3\right)\left(x^2+3x+9\right)+6\left(x+1\right)^2=15$$\Rightarrow x^3-6x^2+12x-8-\left(x^3-27\right)+6\left(x^2+2x+1\right)=15$$\Rightarrow x^3-6x^2+12x-8-x^3+27+6x^2+12x+6=15$$\Rightarrow24x+25=15$$\Rightarrow24x=-10$$\Rightarrow x=\frac{-5}{12}$

Yen Nhi · Answer

Bài 9:a) $-x^2+6x-15=-x^2+6x-9-6=-\left(x^2-6x+9\right)-6=-\left(x-3\right)^2-6$Ta có: $\left(x-3\right)^2\ge0\Rightarrow-\left(x-3\right)^2\le0\Rightarrow-\left(x-3\right)^2-6\le-6$$\Rightarrow-x^2+6x-15$ luôn âm với mọi $x$b) $-9x^2+24x-18=-9x^2+24x-16-2=-\left(9x^2-24x+16\right)-2=-\left(3x-4\right)^2-2$Ta có: $\left(3x-4\right)^2\ge0\Rightarrow-\left(3x-4\right)^2\le0\Rightarrow-\left(3x-4\right)^2-2\le2$$\Rightarrow-9x^2+24x-18$ luôn âm với mọi $x$c) $\left(x-3\right)\left(1-x\right)-2=x\left(1-x\right)-3\left(1-x\right)-2=x-x^2-3+3x-2=-x^2+4x-5$$=-x^2+4x-4-1=-\left(x^2-4x+1\right)-1=-\left(x-1\right)^2-1$Ta có: $\left(x-1\right)^2\ge0\Rightarrow-\left(x-1\right)^2\le0\Rightarrow-\left(x-1\right)^2-1\le-1$$\Rightarrow\left(x-3\right)\left(1-x\right)-2$ luôn âm với mọi xd) $\left(x+4\right)\left(2-x\right)-10=x\left(2-x\right)+4\left(2-x\right)-10=2x-x^2+8-4x-10=-x^2-2x-2$$=-x^2-2x-1-1=-\left(x^2+2x+1\right)-1=-\left(x+1\right)^2-1$Ta có: $\left(x+1\right)^2\ge0\Rightarrow-\left(x+1\right)^2\le0\Rightarrow-\left(x+1\right)^2-1\le-1$$\Rightarrow\left(x+4\right)\left(2-x\right)-10$ luôn âm với mọi $x$Câu trả lời: Bài 9:a) $-x^2+6x-15=-x^2+6x-9-6=-\left(x^2-6x+9\right)-6=-\left(x-3\right)^2-6$Ta có: $\left(x-3\right)^2\ge0\Rightarrow-\left(x-3\right)^2\le0\Rightarrow-\left(x-3\right)^2-6\le-6$$\Rightarrow-x^2+6x-15$ luôn âm với mọi $x$b) $-9x^2+24x-18=-9x^2+24x-16-2=-\left(9x^2-24x+16\right)-2=-\left(3x-4\right)^2-2$Ta có: $\left(3x-4\right)^2\ge0\Rightarrow-\left(3x-4\right)^2\le0\Rightarrow-\left(3x-4\right)^2-2\le2$$\Rightarrow-9x^2+24x-18$ luôn âm với mọi $x$c) $\left(x-3\right)\left(1-x\right)-2=x\left(1-x\right)-3\left(1-x\right)-2=x-x^2-3+3x-2=-x^2+4x-5$$=-x^2+4x-4-1=-\left(x^2-4x+1\right)-1=-\left(x-1\right)^2-1$Ta có: $\left(x-1\right)^2\ge0\Rightarrow-\left(x-1\right)^2\le0\Rightarrow-\left(x-1\right)^2-1\le-1$$\Rightarrow\left(x-3\right)\left(1-x\right)-2$ luôn âm với mọi xd) $\left(x+4\right)\left(2-x\right)-10=x\left(2-x\right)+4\left(2-x\right)-10=2x-x^2+8-4x-10=-x^2-2x-2$$=-x^2-2x-1-1=-\left(x^2+2x+1\right)-1=-\left(x+1\right)^2-1$Ta có: $\left(x+1\right)^2\ge0\Rightarrow-\left(x+1\right)^2\le0\Rightarrow-\left(x+1\right)^2-1\le-1$$\Rightarrow\left(x+4\right)\left(2-x\right)-10$ luôn âm với mọi $x$

Chúng tôi đề xuất

Tài nguyên

Ứng dụng mobile

Bảng xếp hạng

Các khóa học có thể bạn quan tâm

Yêu cầu VIP