Question

1) (x-1)²-9=0

2) (x-10)²-125=x(x-15)-5

3) (x+4)²-4x=(x-3)(x+3)-11

4) (2x-3)²+12x=(4x+3)(x-2)-5

Giúp em với ạ

Answer 1

1) \((x-1)^2-9=0\)

\(⇔(x-1)^2-3^2=0\)

\(⇔(x-4)(x+2)=0\)

\(⇔\left[\begin{array}{} x-4=0\\ x+2=0 \end{array}\right.⇔\left[\begin{array}{} x=4\\ x=-2 \end{array}\right.\)

2) \((x-10)^2-125=x(x-15)-5\)

\(⇔x^2-20x+100-125=x^2-15x-5\)

\(⇔x^2-x^2-20x+15x=-5-100+125\)

\(⇔-5x=20⇔x=-4\)

\(3) (x+4)^2-4x=(x-3)(x+3)-11\)

\(⇔x^2+8x+16-4x=x^2-9-11\)

\(⇔x^2-x^2+8x-4x=-9-11-16\)

\(⇔4x=-36⇔x=-9\)

\(4)(2x-3)^2+12x=(4x-3)(x-2)-5\)

\(⇔4x^2-12x+9+12x=4x^2-11x+6-5\)

\(⇔4x^2-4x^2-12x+12x+11x=6-5-9\)

\(⇔11x=-8 ⇔x=-\dfrac{8}{11}\)