Question

Bài 1.Tìm x biết
a,(x+8)(x+6)=104+x^2
b,(x+1)(x+2)-(x-3)(x+4)=6
c,4x(x-5)-(x-1)(4x-3)=5
d,(3x-4)(x-2)=3x(x-9)-3
e,(x-5)(x-4)-(+1)(x-2)=7
f,5x(x-3)=(x-2)(5x-1)-5

Answer 1

a) \(\left(x+8\right)\left(x+6\right)=104+x^2\Leftrightarrow x^2+6x+8x+48=104+x^2\)

\(\Leftrightarrow x^2+6x+8x-x^2=104-48\Leftrightarrow14x=56\Leftrightarrow x=\dfrac{56}{14}=4\)

vậy \(x=4\)

b) \(\left(x+1\right)\left(x+2\right)-\left(x-3\right)\left(x+4\right)=6\)

\(\Leftrightarrow x^2+2x+x+2-\left(x^2+4x-3x-12\right)=6\)

\(\Leftrightarrow x^2+2x+x+2-x^2-4x+3x+12=6\)

\(\Leftrightarrow2x+14=6\Leftrightarrow2x=6-14=-8\Leftrightarrow x=\dfrac{-8}{2}=-4\)

vậy \(x=-4\)

c) \(4x\left(x-5\right)-\left(x-1\right)\left(4x-3\right)=5\)

\(\Leftrightarrow4x^2-20x-\left(4x^2-3x-4x+3\right)=5\)

\(\Leftrightarrow4x^2-20x-4x^2+3x+4x-3=5\)

\(\Leftrightarrow-13x-3=5\Leftrightarrow-13x=5+3=8\Leftrightarrow x=\dfrac{8}{-13}=\dfrac{-8}{13}\)

vậy \(x=\dfrac{-8}{13}\)

d) \(\left(3x-4\right)\left(x-2\right)=3x\left(x-9\right)-3\)

\(\Leftrightarrow3x^2-6x-4x+8=3x^2-27x-3\)

\(\Leftrightarrow3x^2-6x-4x-3x^2+27x=-3-8\)

\(\Leftrightarrow17x=-11\Leftrightarrow x=\dfrac{-11}{17}\) vậy \(x=\dfrac{-11}{17}\)

e) câu này đề bị thiếu rồi nha bn

f) \(5x\left(x-3\right)=\left(x-2\right)\left(5x-1\right)-5\)

\(\Leftrightarrow5x^2-15x=5x^2-x-10x+2-5\)

\(\Leftrightarrow5x^2-15x-5x^2+x+10x=2-5\)

\(\Leftrightarrow-4x=-3\Leftrightarrow x=\dfrac{-3}{-4}=\dfrac{3}{4}\) vậy \(x=\dfrac{3}{4}\)

Answer 2

a) \(\left(x+8\right)\left(x+6\right)=104+x^2\)

\(\Leftrightarrow x^2+14x+48=104+x^2\)

\(\Leftrightarrow14x=56\)

\(\Rightarrow x=4\)

b) \(\left(x+1\right)\left(x+2\right)-\left(x-3\right)\left(x+4\right)=6\)

\(\Leftrightarrow x^2+3x+2-x^2-7x+12=6\)

\(\Leftrightarrow-4x=-8\)

\(\Rightarrow x=2\)

c) \(4x\left(x-5\right)-\left(x-1\right)\left(4x-3\right)=5\)

\(\Leftrightarrow4x^2-20x-4x^2+3x+4x-3=5\)

\(\Leftrightarrow-13x=8\)

\(\Rightarrow x=\dfrac{-8}{13}\)

d) \(\left(3x-4\right)\left(x-2\right)=3x\left(x-9\right)-3\)

\(\Leftrightarrow3x^2-10x+8=3x^2-27x-3\)

\(\Leftrightarrow17x=-11\)

\(\Rightarrow x=\dfrac{-11}{17}\)

e) \(\left(x-5\right)\left(x-4\right)-\left(x+1\right)\left(x-2\right)=7\)

\(\Leftrightarrow x^2-9x+20-x^2+x+2=7\)

\(\Leftrightarrow-8x=-15\)

\(\Rightarrow x=\dfrac{15}{8}\)

f) \(5x\left(x-3\right)=\left(x-2\right)\left(5x-1\right)-5\)

\(\Leftrightarrow5x^2-15x=5x^2-11x+2-5\)

\(\Leftrightarrow-4x=-3\)

\(\Rightarrow x=\dfrac{3}{4}\)