( X:10) + 37 = 6025 x X- 15x X- 15 x X=72
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e) Ta có: \(E=\left(3x+2\right)\left(3x-5\right)\left(x-1\right)\left(9x+10\right)+24x^2\)
\(=\left(9x^2-15x+6x-10\right)\left(9x^2+10x-9x-10\right)+24x^2\)
\(=\left(9x^2-10-9x\right)\left(9x^2-10+x\right)+24x^2\)
\(=\left(9x^2-10\right)^2-8x\left(9x^2-10\right)-9x^2+24x^2\)
\(=\left(9x^2-10\right)^2-8x\left(9x^2-10\right)+15x^2\)
\(=\left(9x^2-10\right)^2-3x\left(9x^2-10\right)-5x\left(9x^2-10\right)+15x^2\)
\(=\left(9x^2-10\right)\left(9x^2-3x-10\right)-5x\left(9x^2-10-3x\right)\)
\(=\left(9x^2-3x-10\right)\left(9x^2-5x-10\right)\)
= ( -25) x 1 +72 x (-25) + (-25) x27
= (- 25) x ( 1 + 72 + 27 )
= (-25) x 100
=-2500
b
c 37 x ( 25 + 37 ) - 27 x ( 37 + 25 )
= 37 x 25 + 37 x 37 -27x37 -27x25
= ( 37 x25 -27x25 )+(37x37-27+37)
=25 x ( 37 -27 ) + 37 x (37 - 27)
= 25 x10 + 37x10
= 250 + 370
= 770
a) =-25.( 1+72+27)
=-25.100= - 2500
b) = -36.45 + (-36) . 15 - (-36) . 40
= - 36. ( 45+15-40)
= -36 . 20= -720
c) =37.62 - 27 .62
= 62. ( 37 - 27 )
= 62 . 10
= 620
a (X:10)+37=60
X:10=23
X=2,3
b 25xX-15xX=72
X(x25-15)=72
Xx10=72
X=7,2
c 138-(Xx5)=38
Xx5=100
X=20
d (Xx9):52=18
Xx9=936
X=104
e 52xX+48xX=100
Xx(52+48)=100
Xx100=100
X=1
f 623xX-123xX=1000
Xx(623-123)=1000
Xx500=1000
X=2
g Xx16+84xX=700
Xx(16+84)=700
Xx100=700
X=7
h 236xX-Xx36=2000
Xx(236-26)=2000
Xx200=2000
X=10
i 216:X+34:X=10
(216+34):X=10
250:X=10
X=25
f 2125:X-125:X=100
(2125-125):X=100
2000:X=100
X=20
\(A=x^{10}-14x^9-x^9+14x^8+x^8-14x^7-x^7...-x+14+1\)
\(A=x^9\left(x-14\right)-x^8\left(x-14\right)+x^7\left(x-14\right)-...-x\left(x-14\right)+1\)
\(A=1\) (Do x=14)
Ta có x=14 suy ra x+1=15
Do đó thay x+1 vào H(x), ta được:
H(14)= x10 - (x+1)x9 +(x+1)x8-(x+1)x7+...+ (x+1)x2 - (x+1)x + x+1
H(14)= x^10 - x^10 -x^9 +x^8- x^8-x^7 +....+ x^3 +x^2 -x^2-x+x +1
Hay H(14)=1
Đặt Q(x) = x9 - x8 + x7 - ... + x - 1 thì (x + 1) * Q(x) = (x + 1) * (x9 - x8 + x7 - ... + x - 1) = x10 - 1 \(\Rightarrow\left(14+1\right)\cdot Q\left(14\right)=14^{10}-1\)
Dễ thấy: H(x) = x10 - 15* Q(x) \(\Rightarrow H\left(14\right)=14^{10}-\left(14^{10}-1\right)=1\)
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