Đáp án + Giải thích các bước giải:
1, `(x-5)^2 - 81(2x-3)^2 = 0`
`=> x^2 - 10x + 25 - 324x^2 + 972x - 729 = 0`
`=> -323x^2 + 962x - 704 = 0`
`=> -(323x^2-962x+704) = 0`
`=> -(323x^2-418x-544x+704) = 0`
`=> -[19x(17x-22)-32(17x-22)] = 0`
`=> -(17x-22)(19x-32) = 0`
`=>` \(\left[ \begin{array}{l}17x-22=0\\19x-32=0\end{array} \right.\)
`=>` \(\left[ \begin{array}{l}x=\dfrac{22}{17}\\x=\dfrac{32}{19}\end{array} \right.\)
Vậy `S = {22/17,32/19}`
2, `(x+2)^3-(x-3)^3=0`
`=> x^3 + 6x^2 + 12x + 8 + x^3 - 9x^2 + 27x - 27 = 0`
`=> 2x^3 - 3x^2 + 39x - 19 = 0`
`=> 2x^3 - x^2 - 2x^2 + x + 38x - 19 = 0`
`=> x^2(2x-1)-x(2x-1)+19(2x-1)=0`
`=> (2x-1)(x^2-x+19) = 0`
`x^2-x+19=[x^2-2*x*1/2+(1/2)^2]+75/4 = (x-1/2)^2 + 75/4`
Vì `(x-1/2)^2 \ge 0 => (x-1/2)^2 + 75/4 \ge 75/4 > 0`
`=> 2x - 1= 0`
`=> 2x = 1`
`=> x = 1/2`
Vậy `S = {1/2}`
