Toán Lớp 8: Tìm x : `a)` `2x(x+7) -2=18` `b)` `2x(x-5)=4(x-5)`

Question

Toán Lớp 8:  Tìm x : a) 2x(x+7) -2=18 b) 2x(x-5)=4(x-5)

buianhtuan · Answer

$  $   a,   2x(x+7)-2=18   &harr;2x^2+14x-20=0   &harr; x^2+7x-10=0   &harr; (x+7/2)^2  = 89/4   th1 :   x+7/2= sqrt{89/4}   &harr; x=(-7+ sqrt{89})/2   th2 :   x+7/2=- sqrt{89/4}   &harr; x=(-7- sqrt{89})/2   Vậy  x=(-7+ sqrt{89})/2, x=(-7- sqrt{89})/2   b,   2x(x-5)=4(x-5)   &harr; 2x(x-5)-4(x-5)=0   &harr; (x-5)(2x-4)=0   th1 :   x-5=0   &harr;x=5   th2 :   2x-4=0   &harr;2x=4   &harr;x=2   Vậy x=5,x=2

dinhcongson · Answer

Giải đáp: a) x=(-7+ sqrt{89})/2 hoặc x=-(7+ sqrt{89})/2 b) x=5 hoặc x=2 Lời giải và giải thích chi tiết: a) 2x(x+7)-2=18 <=>2x^2+14x-2-18=0 <=>2x^2+14x-20=0 <=>x^2+7x-10=0 <=>(x^2+2.x.(7)/2+(49)/(4))-10-(49)/4=0 <=>(x+7/2)^2-(89)/4=0 <=>(x+7/2)^2=(89)/4 <=> ( left[ begin{array}{l}x+ dfrac{7}{2}= sqrt{ dfrac{89}{4}} x+ dfrac{7}{2}=- sqrt{ dfrac{89}{4}} end{array} right. ) <=> ( left[ begin{array}{l}x= dfrac{-7+ sqrt{89}}{2} x=- dfrac{7+ sqrt{89}}{2} end{array} right. ) Vậy x=(-7+ sqrt{89})/2 hoặc x=-(7+ sqrt{89})/2 b) 2x(x-5)=4(x-5) <=>2x(x-5)-4(x-5)=0 <=>2(x-5)(x-2)=0 <=> ( left[ begin{array}{l}x-5=0 x-2=0 end{array} right. ) <=> ( left[ begin{array}{l}x=5 x=2 end{array} right. ) Vậy x=5 hoặc x=2