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a)\(\left(5x-1\right)^2-\left(5x-4\right)\left(5x+4\right)=7\)
\(\Leftrightarrow25x^2-10x+1-25x^2+16=7\)
\(\Leftrightarrow-10x=-10\)
\(\Leftrightarrow x=1\)
b) k hiểu đề
\(\left(9x-1\right)^2-2\left(9x-1\right)\left(5x-1\right)+\left(5x-1\right)^2=\left(9x-1-5x+1\right)^2=\left(14x\right)^2=196x^2\)
a) \(\left(4x-1\right)^2-\left(3x+2\right)\left(3x-2\right)=\left(7x-1\right)\left(x+2\right)+\left(2x+1\right)^2-\left(4x^2+7\right)\)(1)
\(\Leftrightarrow\left(16x^2-8x+1\right)-\left(9x^2-4\right)=\left(7x^2+14x-x-2\right)+\left(4x^2+4x+1\right)-\left(4x^2+7\right)\)
\(\Leftrightarrow16x^2-8x+1-9x^2+4=7x^2+13x-2+4x^2+4x+1-4x^2-7\)
\(\Leftrightarrow7x^2-8x+5=7x^2+17x-8\)
\(\Leftrightarrow7x^2-8x-7x^2-17x=-8-5\)
\(\Leftrightarrow-25x=-13\)
\(\Leftrightarrow x=\dfrac{13}{25}\)
Vậy tập nghiệm phương trình (1) là \(S=\left\{\dfrac{13}{25}\right\}\)
a)Ta có:
\(\left(x-2\right)^2-\left(x-3\right)\left(x-1\right)\\ =x^2-4x+4-x^2+4x-3\\ =1\)
Vậy biểu thức \(\left(x-2\right)^2-\left(x-3\right)\left(x-1\right)\)không phụ thuộc vào biến
b) Ta có:
\(\left(x-1\right)^3-\left(x+1\right)^3+6\left(x+1\right)\left(x-1\right)\\ =x^3-3x^2+3x-1-x^3-3x^2-3x-1+6x^2-6\\ =-8\)
Vậy.....
c) Ta có:
\(\left(x-3\right)\left(x+3\right)\left(x^2+9\right)-\left(x^2-2\right)\left(x^2+2\right)\\ =\left(x^2-9\right)\left(x^2+9\right)-x^4+4\\ =x^4-81-x^4+4=-77\)
Vậy....
d) Ta có: \(\left(3x+1\right)^2-2\left(3x+1\right)\left(3x-5\right)+\left(3x-5\right)^2\\ =\left(3x+1-3x+5\right)^2\\ =6^2=36\)
Vậy....
a) \(A=\left(3x+2\right)^2-9x\left(x+1\right)\)
\(A=9x^2+12x+4-9x^2-9x\)
\(A=3x+4\)
\(B=\left(2x-1\right)^2-2\left(2x-1\right)\left(5x-1\right)+\left(5x-1\right)^2\)
\(B=\left[2x-1-\left(5x-1\right)\right]^2\)
\(B=\left(2x-1-5x+1\right)^2\)
\(B=\left(-3x\right)^2\)
\(B=9x^2\)
a) 5.(2x-1)2+4.(x-1).(x+3-2).(5-3x)2
=20x2-20x+5+36x4-120x3+64x2+120x-100
=36x4+(-20x+120x)+(5-100)+(64x2+20x2)-120x3
=36x4+100x-95+84x2-120x3
b,c,d bn tự tính nhé bậc cao qá nên khó tính
-3x^3+5x^2-9x+15 -3x-5 x^2 -3x^3-5x^2 - 10x^2-9x+15 -(10/3)x 10x^2+(50/3)x - -(23/3)x+15 +23/9 -(23/3)x-115/9 - 250/9
Chả biết có sai ko @@
x^4-2x^3 +2x-1 x^2-1 x^2-2x x^4 -x^2 - -2x^3+x^2+2x-1 -2x^3 +2x - x^2-1 +1 x^2-1 - 0
a) \(\left(9x-1\right)^2+\left(1-5x\right)^2+2\left(9x-1\right)\left(1-5x\right)\)
\(=\left(9x-1\right)^2+2\left(9x-1\right)\left(1-5x\right)+\left(1-5x\right)^2\)
\(=\left(9x-1+1-5x\right)^2=\left(4x\right)^2\)
b) \(x^2\left(x+4\right)\left(x-4\right)-\left(x^2+1\right)\left(x^2-1\right)\)
\(=x^2\left(x^2-16\right)-\left(x^4-1\right)\)
\(=x^4-16x^2-x^4+1=-16x^2+1\)