tìm x
x+15+4.25=115
4.25 x ( x+41.53) -125=53.5
53.2 : ( x - 3.5 ) + 45.8 = 99
( x + 1 )+(x+4)+(x + 7)+(x + 10)....+(x + 28 )= 115
( x + 1 )+(x+4)+(x + 7)+(x + 10)....+(x + 28 )= 115
=> 10x + (1 + 4 + 7 + ..... + 28) = 115
=> 10x + 145 = 115
=> 10x = -30
=> x = -3
Tìm x \in \mathbb{N} thỏa mãn 18 \vdots x, 315 \vdots x và 5 < x \le 11.
a.x=9
b.x=7
c.x=11
d.không có giá trị nào của x
ta có :18=2.32; 135=32 .5.7
UCLN(18,315)=32=9
B(9)={0;9;18;27;....}
mà 5 < x ≤11
⇒x= 9 (tm)
4.25 x X > 17.5 x 4.25
Tìm số tự nhiên bé nhất khi thay vào x thi được:
\(\dfrac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}\)
\(M=\dfrac{3^6.45^4-15^4.9^4}{27^4.25^3+7.45^6}\)
\(=\dfrac{3^{14}\cdot5^4-5^4\cdot3^{12}}{3^{12}\cdot5^6+7\cdot3^{12}\cdot5^6}=\dfrac{3^{12}\cdot5^4\left(3^2-1\right)}{3^{12}\cdot5^6\left(1+7\right)}=\dfrac{1}{25}\)
\(\dfrac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}\)
\(\dfrac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}=\dfrac{3^6.3^85^4-3^{13}.5^{13}.5^{-9}}{3^{12}.5^6+3^{12}.5^6}\)
\(=\dfrac{3^{14}.5^4-3^{13}.5^4}{2.3^{12}.5^6}=\dfrac{3^{13}.5^4\left(3-1\right)}{2.3^{12}.5^6}\)
\(=\dfrac{3.2}{2.5^2}=\dfrac{3}{25}\)
\(\frac{3^6.45^4-15^3.5^{-9}}{27^4.25^3+45^6}\)
\(\frac{3^6.45^4-15^3.5^9}{27^4.25^3+45^6}\)
\(=\dfrac{3^6\cdot3^8\cdot5^4-3^3\cdot5^3\cdot5^9}{3^{12}\cdot5^6+3^{12}\cdot5^6}=\dfrac{5^4\cdot3^3\cdot\left(3^{11}-5^8\right)}{3^{12}\cdot5^6\cdot2}=\dfrac{-106739}{3^9\cdot5^2}\)
\(\dfrac{3^6.45^4-15^{13}.5^{-9}}{27^4.25^3+45^6}\)?
\(=\dfrac{3^6\cdot\left(3^2\right)^4\cdot5^4-5^{13}\cdot3^{13}\cdot5^{-9}}{3^{12}\cdot5^6+\left(3^2\right)^6\cdot5^6}\)
\(=\dfrac{3^{14}\cdot5^4-5^4\cdot3^{13}}{3^{12}\cdot5^6+3^{12}\cdot5^6}=\dfrac{3^{13}\cdot5^4\cdot2}{2\cdot3^{12}\cdot5^6}=\dfrac{3}{5^2}=\dfrac{3}{25}\)