$6$
$a$) $A = 1,7 + |3,4 -x|$
Vì : $|3,4 - x|$ $≥$ $0$ $∀$ $x$
$⇒$ $A ≥ 1,7 + 0 = 1,7$
Dấu "$=$" khi $3,4-x=0⇔x=3,4$
Vậy $A$ đạt $GTNN=1,7$ khi $x=3,4$.
$b$) $B = |x+2,8| - 3,5$
Vì : $|x+2,8|$ $≥$ $0$ $∀$ $x$
$⇒$ $B ≥ 0 - 3,5 = -3,5$
Dấu " $=$ " khi $x+2,8=0⇔ x = -2,8$
Vậy $B$ đạt $GTNN=-3,5$ khi $x=-2,8$
$c$) $C = |4,3 - x| + 3,7$
Vì : $|4,3 - x|$ $≥$ $0$ $∀$ $x$
$⇒ C ≥ 0 + 3,7 = 3,7$
Dấu " $=$ " khi $4,3-x=0⇔x=4,3$
Vậy $C$ đạt $GTNN=3,7$ khi $x=4,3$
$7$.
$a$) $A = 3^2.3^3 + 2^3.2^2$
$⇔ A = 3^5 + 2^5$
$⇔ A = 275$
$b$) $B = 3.4^2 - 2^2 .3$
$⇔ B = 3(4^2 - 2^2)$
$⇔ B = 3.12$
$⇔ B = 36$
$c$) $D=(2^9 . 3 + 2^9 .5) - 2^{12}$
$⇔ D = 2^9.8 - 2^{12}$
$⇔ D = 2^9.(8 - 8)$
$⇔ D = 0$
$d$) $E = 2 + 2^2 + 2^3 + ... + 2^{100}$
$⇔ 2E = 2^2 + 2^3 + 2^4 + ... + 2^{101}$
$⇔ 2E - E = ( 2^2 + 2^3 + 2^4 + ... + 2^{101})-( 2 + 2^2 + 2^3 + ... + 2^{100})$
$⇔ E = 2^{101} - 2$
$e$) $F =1 + 3^1 + 3^2 + .... + 3^{100}$
$⇔ 3F = 3 + 3^2 + 3^3 + ... + 3^{101}$
$⇔ 3F-F= (3 + 3^2 + 3^3 + ... + 3^{101})-(1 + 3^1 + 3^2 + .... + 3^{100})$
$⇔ 2F = 3^{101} - 1$
$⇔ F = \dfrac{3^{101}-1}{2}$
$f$) $G= 5 + 5^3 + 5^5 + ... + 5^{99}$
$⇔ 5^2G = 5^3 + 5^5 + 5^7 + ... + 5^{101}$
$⇔ 25G - G = (5^3 + 5^5 + 5^7 + ... + 5^{101})-(5 + 5^3 + 5^5 + ... + 5^{99})$
$⇔ 24G = 5^{101} - 5$
$⇔ G = \dfrac{5^{101}-5}{24}$
