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Bài 4 :
Thay x=y+5 , ta có :
a ) ( y+5)*(y5+2)+y*(y-2)-2y*(y+5)+65
=(y+5)*(y+7)+y^2-2y-2y^2-10y+65
=y^2+7y+5y+35-y^2-2y-2y^2-10y+65
= 100
Bài 5 :
A = 15x-23y
B = 2x-3y
Ta có : A-B
= ( 15x -23y)-(2x-3y)
=15x-23y-2x-3y
=13x-26y
=13x*(x-2y) chia hết cho 13
=> Nếu A chia hết cho 13 thì B chia hết cho 13 và ngược lại
Bài 1:
Ta có:
\(A=9x^4-15x^3-6x^2+5=3x^2\left(3x^2-5x\right)-6x^2+5=3x^2.2-6x^2+5=6x^2-6x^2+5=5\)
Vậy, \(A=5\)
Bài 2: Ta có:
\(3^{15}+3^{16}+3^{17}=3^{15}+3^{15}.3+3^{15}.3^2=3^{15}.\left(1+3+3^2\right)=3^{15}.13\)
\(\Rightarrow3^{15}.13\) chia hết cho \(13\)
Do đó: \(3^{15}+3^{16}+3^{17}\) chia hết cho \(13\)
x=7
=>x+1=8
=> A= x^15 - 8x^14 + 8x^13 - 8x^12 +....- 8x^2 + 8x - 5
=x15-(x+1)x14+(x+1)x13-(x+1)x12+...-(x+1)x2+(x+1)x-5
=x15-x15-x14+x14+x13-x13-x12+...-x3-x2+x2+x-5
=x-5
=>A=7-5=2
Vậy A=2 khi x=7
\(B=x^{15}-8x^{14}+8x^{13}-8x^{12}+...+8x-5\)
\(=x^{15}-\left(x+1\right)x^{14}+\left(x+1\right)x^{13}-\left(x+1\right)x^{12}+...+\left(x+1\right)x-x+2\)
\(=x^{15}-x^{15}-x^{14}+x^{14}+x^{13}-x^{13}-x^{12}+...+x^2+x-x+2\)
\(=2\)
x=11 suy ra 12=x+1 thay vào A ta có:
A=x^17- (x+1)x^16 + (x+1)x^15 - (x+1)x^14 + .....- (x+1)x^2+(x+1)x -1
= x^17 - x^17 -x^16 + x^16 + x^15 - x^15 - x^14 +.....- x^3 -x^2 + x^2 +x -1
= x-1= 11-1=10
2A = 2^18 - 2^17 - 2^15 - 2^14 - 2^13 - ... - 2^2 - 2
2A - A = A = ( 2^18 - 2^17 - 2^16 - 2^15 - 2^14 - 2^13 - ... - 2^2 - 2 ) - ( 2^17 - 2^16 - 2^15 - 2^14 - 2^13 - ... -2 - 1 )
A = 2^18 - 2^17 - 2^16 - 2^15 - 2^14 - 2^13 - ... - 2^2 - 2 - 2^17 + 2^16 + 2^15 + 2^14 + 2^13 + ... + 2 + 1
A = 2^18 - 2^17 - 2^17 + 1
A = 2^18 - 2 . 2^17 + 1
A =2^17- 2^16-...-2-2^0
Ax2= 2^18-2^17-.....-2^2-2^1
Ax2-A=2^18-2^17-...-2^2-2^1-2^17+2^16+....+2^1+1
A=2^18-2^17-2^17+1
A=2^18-2^17X2+1
A=2^18-2^18+1
A=0+1
A=1
20) -5-(x + 3) = 2 - 5x ⇔ -5 - x - 3 = 2 -5x ⇔ 4x = 10 ⇔ x = \(\frac{5}{2}\)
Vậy...
\(=\dfrac{\left(3\cdot\dfrac{5}{6}+\dfrac{12}{7}:\dfrac{5}{6}:\dfrac{25}{36}\right)}{\dfrac{5}{6}:\dfrac{12}{7}}=\dfrac{9559}{1750}:\dfrac{35}{72}=\dfrac{688248}{61250}\)
Mn giúp mình với ạ, mik cần gấp
\(H=-3\left(-\dfrac{13}{15}-\dfrac{17}{21}\right)-\dfrac{13}{5}+\dfrac{17}{7}+\left(12-\dfrac{35}{3}\right):\dfrac{7}{6}\)
\(=\dfrac{13}{5}+\dfrac{17}{7}-\dfrac{13}{5}+\dfrac{17}{7}+\dfrac{1}{3}\cdot\dfrac{6}{7}\)
\(=\dfrac{34}{7}+\dfrac{2}{7}=\dfrac{36}{7}\)