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a/ \(x=99\Rightarrow100=x+1\)
\(A=x^5-\left(x+1\right)x^4+\left(x+1\right)x^3-\left(x+1\right)x^2+\left(x+1\right)x-9\)
\(=x^5-x^5-x^4+x^4+x^3-x^3-x^2+x^2+x-9\)
\(=x-9=99-9=90\)
b/ Tương tự \(20=x-1\)
\(B=x^6-\left(x-1\right)x^5-\left(x-1\right)x^4-\left(x-1\right)x^3-\left(x-1\right)x^2-\left(x-1\right)x+3\)
\(=x^6-x^6+x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x+3\)
\(=x+3=24\)
c/ \(26=x+1;27=x+2;47=2x-3;77=3x+2;50=2x\)
\(C=x^7-\left(x+1\right)x^6+\left(x+2\right)x^5-\left(2x-3\right)x^4-\left(3x+2\right)x^3+2x.x^2+x-24\)
\(=x-24=1\)
a/ x=99⇒100=x+1x=99⇒100=x+1
A=x5−(x+1)x4+(x+1)x3−(x+1)x2+(x+1)x−9A=x5−(x+1)x4+(x+1)x3−(x+1)x2+(x+1)x−9
=x5−x5−x4+x4+x3−x3−x2+x2+x−9=x5−x5−x4+x4+x3−x3−x2+x2+x−9
=x−9=99−9=90=x−9=99−9=90
b/ Tương tự 20=x−120=x−1
B=x6−(x−1)x5−(x−1)x4−(x−1)x3−(x−1)x2−(x−1)x+3B=x6−(x−1)x5−(x−1)x4−(x−1)x3−(x−1)x2−(x−1)x+3
=x6−x6+x5−x5+x4−x4+x3−x3+x2−x2+x+3=x6−x6+x5−x5+x4−x4+x3−x3+x2−x2+x+3
=x+3=24=x+3=24
c/ 26=x+1;27=x+2;47=2x−3;77=3x+2;50=2x26=x+1;27=x+2;47=2x−3;77=3x+2;50=2x
C=x7−(x+1)x6+(x+2)x5−(2x−3)x4−(3x+2)x3+2x.x2+x−24C=x7−(x+1)x6+(x+2)x5−(2x−3)x4−(3x+2)x3+2x.x2+x−24
=x−24=1=x−24=1
b \(\Leftrightarrow x^3\left(x-2\right)+10x\left(x-2\right)=0\)
\(\Leftrightarrow x\left(x-2\right)=0\)
hay \(x\in\left\{0;2\right\}\)
c: \(\Leftrightarrow\left(2x-3-x-5\right)\left(2x-3+x+5\right)=0\)
=>(x-8)(3x+2)=0
=>x=8 hoặc x=-2/3
d: \(\Leftrightarrow x^2\left(x-1\right)-4\left(x-1\right)^2=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2-4x+4\right)=0\)
=>x=2 hoặc x=1
e: \(\Leftrightarrow x\left(x^2-11x+30\right)=0\)
=>x(x-5)(x-6)=0
hay \(x\in\left\{0;5;6\right\}\)
b: \(\Leftrightarrow x\left(x^3-2x^2+10x-20\right)=0\)
\(\Leftrightarrow x\left(x-2\right)=0\)
hay \(x\in\left\{0;2\right\}\)
c: \(\Leftrightarrow\left(2x-3-x-5\right)\left(2x-3+x+5\right)=0\)
=>(x-8)(3x+2)=0
hay \(x\in\left\{8;-\dfrac{2}{3}\right\}\)
d: \(\Leftrightarrow x^2\left(x-1\right)-4\left(x-1\right)^2=0\)
\(\Leftrightarrow\left(x-1\right)\left(x^2-4x+4\right)=0\)
\(\Leftrightarrow\left(x-1\right)\left(x-2\right)^2=0\)
=>x=1 hoặc x=2
Câu này bạn đã đăng rồi và có người trả lời rồi nhé, abnj xem lại câu hỏi nha :
Câu hỏi của ngố ngố - Toán lớp 8 | Học trực tuyến
1. \(x^4-2x^2+1=\left(x^2-1\right)^2\)
2. \(x^2+5x+\dfrac{25}{4}=x^2+2.x.\dfrac{5}{2}+\left(\dfrac{5}{2}\right)^2=\left(x+\dfrac{5}{2}\right)^2\)
3. \(16x^2-8x+1=\left(4x-1\right)^2\)
4. \(x^2+x-y^2+y=\left(x-y\right)\left(x+y\right)+\left(x+y\right)=\left(x-y+1\right)\left(x+y\right)\)
5. \(\dfrac{1}{4}x^2-\dfrac{4}{9}y^2=\left(\dfrac{1}{2}x-\dfrac{2}{3}y\right)\left(\dfrac{1}{2}x+\dfrac{2}{3}y\right)\)
6. \(a^2-2ab+b^2-x^2=\left(a-b\right)^2-x^2=\left(a-b-x\right)\left(a-b+x\right)\)
7. \(4x^2-20x+25-y^2=\left(2x-5\right)^2-y^2=\left(2x-5-y\right)\left(2x-5+y\right)\)
a) Có x = 99 => x+1 = 100
A = x5 - (x+1)x4 + (x+1)x3 + (x+1)x2 + (x+1)x - 9
= x5 - x5 + x4 - x4 + x3 - x3 + x2 - x2 + x - 9
= x - 9
=> A = 90
b) Chữa đề: x6 - 20x5 - 20x4 - 20x3 - 20x2 - 20x + 3
Có: x = 21 => x-1 = 20
B = x6 - (x-1)x5 - (x-1)x4 - (x-1)x3 - (x-1)x2 - (x-1)x + 3
= x6 - x6 + x5 - x5 + x4 - x4 + x3 - x3 + x2 - x + 3
= x + 3
=> B = 24