1 tính giá trị biết
A = ( x-3 ) . ( x+7 – ( 2x-5 ) . ( x-1) với x = 0 ; x=1
B = (3x+5).(2x-1)+(4x-1).(3x+2) với |x|= 2
C = (2x+y).(2z+y)+(x-y).(y-z) với x=1 ; y=1 ; z=1
2 tìm x biết
a (3x-1).(2x+7)-(x+1).(6x-5) = 16
b (10x+9)x – (5x-1).(2x+3)=8
c (x ² – 7 ) . ( x + 2 ) – ( 2x-1) . ( x -14 ) + ( x-2 ) . x = 0
Đáp án:
$1)
A(0)=-26\\
\Rightarrow A(1)=-16\\
B(2)=89\\
\Rightarrow B(-2)=41\\
C=9\\
2)
a) x=1\\
b)x=\dfrac{-5}{4}\\$
Giải thích các bước giải:
$1)
A=(x-3)(x+7)-(2x-5)(x-1)\\
=x^2+7x-3x-21-(2x^2-2x-5x+5)\\
=x^2+7x-3x-21-2x^2+2x+5x-5\\
=(x^2-2x^2)+(7x-3x+2x+5x)+(-21-5)\\
=-x^2+11x-26\\
\Rightarrow A(0)=-0^2+11.0-26=-26\\
\Rightarrow A(1)=-1^2+11.1-26=-1+11-26=-16\\
|x|=2\Rightarrow x=\pm 2\\
B=(3x+5)(2x-1)+(4x-1)(3x+2)\\
=6x^2-3x+10x-5+12x^2+8x-3x-2\\
=(6x^2+12x^2)+(-3x+10x+8x-3x)+(-5-2)\\
=18x^2+12x-7\\
\Rightarrow B(2)=18.2^2+12.2-7=89\\
\Rightarrow B(-2)=18.(-2)^2+13.-2-7=41\\
C=(2.1+1)(2.1+1)+(1-1)(1-1)\\
=3.3+0=9\\
2)
a) (3x-1)(2x+7)-(x+1)(6x-5)=16\\
\Leftrightarrow 6x^2+21x-2x-7-(6x^2-5x+6x-5)=16\\
\Leftrightarrow 6x^2+21x-2x-7-6x^2+5x-6x+5=16\\
\Leftrightarrow 18x-2=16\\
\Leftrightarrow 18x=18\\
\Leftrightarrow x=1\\
b) (10x+9)x-(5x-1)(2x+3)=8\\
\Leftrightarrow 10x^2+9x-(10x^2+15x-2x-3)=8\\
\Leftrightarrow 10x^2+9x-10x^2-15x+2x+3=8\\
\Leftrightarrow -4x+3=8\\
\Leftrightarrow -4x=5\\
\Leftrightarrow x=\dfrac{-5}{4}\\$