Question

Giải pt:

a, \(\dfrac{1}{27}.\left(x-3\right)^2-\dfrac{1}{125}.\left(x-5\right)^3=0\)

b, \(125x^3-\left(2x+1\right)^3-\left(3x-1\right)^3=0\)

c, \(\left(x-3\right)^3+\left(x+1\right)^3=8.\left(x-1\right)^3\)

Answer 1

a: \(\Leftrightarrow\left(\dfrac{1}{3}x-1\right)^3=\left(\dfrac{1}{5}x-1\right)^3\)

=>1/3x-1=1/5x-1

=>2/15x=0

hay x=0

b: Đặt 2x+1=a; 3x-1=b

Theo đề, ta có \(\left(a+b\right)^3-a^3-b^3=0\)

=>3ab(a+b)=0

=>5x(2x+1)(3x-1)=0

hay \(x\in\left\{0;-\dfrac{1}{2};\dfrac{1}{3}\right\}\)

c: Đặt x-3=a; x+1=b

Theo đề, ta có: \(\left(a+b\right)^3=a^3+b^3\)

=>3ab(a+b)=0

=>(x-3)(x+1)(2x-2)=0

hay \(x\in\left\{3;-1;1\right\}\)