Toán Lớp 8: giải phương trình: 1) (x-3)(x-2)(x+1)(x+2)=60 2) (x² +14x+24)(x²+11x+24)=4x²

Question

Toán Lớp 8:  giải phương trình: 1) (x-3)(x-2)(x+1)(x+2)=60 2) (x² +14x+24)(x²+11x+24)=4x²

tuanh · Answer

$ begin{array}{l}  left( {x - 3}  right) left( {x - 2}  right) left( {x + 1}  right) left( {x + 2}  right) = 60     Leftrightarrow  left( {x - 3}  right) left( {x + 2}  right) left( {x - 2}  right) left( {x + 1}  right) = 60     Leftrightarrow  left( {{x^2} - x - 6}  right) left( {{x^2} - x - 2}  right) = 60     Leftrightarrow  left( {t - 2}  right) left( {t + 2}  right) = 60 left( {t = {x^2} - x - 4}  right)     Leftrightarrow {t^2} - 4 - 60 = 0     Leftrightarrow {t^2} = 64     Leftrightarrow  left[  begin{array}{l} t = 8   t =  - 8  end{array}  right.     Leftrightarrow  left[  begin{array}{l} {x^2} - x - 4 = 8   {x^2} - x - 4 =  - 8  end{array}  right.  Leftrightarrow  left[  begin{array}{l} {x^2} - x - 12 = 0   {x^2} - x + 4 = 0(PTVN)  end{array}  right.     Rightarrow {x^2} - x - 12 = 0     Leftrightarrow  left( {x + 3}  right) left( {x - 4}  right) = 0     Leftrightarrow  left[  begin{array}{l} x =  - 3   x = 4  end{array}  right.  end{array}$     2)   $ begin{array}{l}  left( {{x^2} + 14x + 24}  right) left( {{x^2} + 11x + 24}  right) = 4{x^2}    Leftrightarrow  left( {t + 14x}  right) left( {t + 11x}  right) = 4{x^2} left( {{x^2} + 24 = t}  right)    Leftrightarrow {t^2} + 25xt + 150{x^2} = 0    Leftrightarrow {t^2} + 10xt + 15xt + 150{x^2} = 0    Leftrightarrow t left( {t + 10x}  right) + 15x left( {t + 10x}  right) = 0    Leftrightarrow  left( {t + 10x}  right) left( {t + 15x}  right) = 0    Leftrightarrow  left[  begin{array}{l} t = - 10x   t = - 15x  end{array}  right.  Leftrightarrow  left[  begin{array}{l} {x^2} + 24 = - 10x   {x^2} + 24 = - 15x  end{array}  right. left( {x < 0}  right)    Leftrightarrow  left[  begin{array}{l} {x^2} + 10x + 24 = 0   {x^2} + 15x + 24 = 0  end{array}  right.    Leftrightarrow  left[  begin{array}{l}  left( {x + 6}  right) left( {x + 4}  right) = 0   x =  dfrac{{ - 15 +  sqrt {129} }}{2}   x =  dfrac{{ - 15 -  sqrt {129} }}{2}  end{array}  right.    Leftrightarrow  left[  begin{array}{l} x = - 4   x = - 6   x =  dfrac{{ - 15 +  sqrt {129} }}{2}   x =  dfrac{{ - 15 -  sqrt {129} }}{2}  end{array}  right.  end{array}$