Tìm Min A=2x^2-8x-10
Tìm Max B=9x-3x^2
Rút gọn biểu thức: 3.(2^2+1).(2^4+1).(2^8+1).(2^16+1)
Giups mk vs
hứa vote 5 sao
Tìm Min A=2x^2-8x-10
Tìm Max B=9x-3x^2
Rút gọn biểu thức: 3.(2^2+1).(2^4+1).(2^8+1).(2^16+1)
Giups mk vs
hứa vote 5 sao
+ Ta có:
`A=2x^2-8x-10`
`A=2(x+\frac{-8}{2.2})^2+\frac{4.2.(-10)-(-8)^2}{4.2}`
`A>=\frac{4.2.(-10)-(-8)^2}{4.2}=-18`
Dấu $”=”$ xảy ra `<=>x=-\frac{-8}{2.2}=2`
Vậy $Min_A=-18$ tại `x=2`
+ Ta có:
`B=9x-3x^2`
`=-3(x^2-3x)`
`=-3(x^2-3x+\frac{9}{4})+\frac{27}{4}`
`=-3(x-\frac{3}{2})^2+\frac{27}{4}<=\frac{27}{4}`
Dấu $”=”$ xảy ra `<=>x=\frac{3}{2}`
Vậy $Max_B=\dfrac{27}{4}$ tại `x=\frac{3}{2}`
+ Ta có:
`3(2^2+1)(2^4+1)(2^8+1)(2^{16}+1)`
`=(2^2-1)(2^2+1)(2^4+1)(2^8+1)(2^{16}+1)`
`=(2^4-1)(2^4+1)(2^8+1)(2^{16}+1)`
`=(2^8-1)(2^8+1)(2^{16}+1)`
`=(2^{16}-1)(2^{16}+1)`
`=2^{32}-1`
Đáp án:
a,A=2x² – 8x -10
A=2.(x² – 4x -5)
A= 2.(x² -4x +4 -9)
A= 2(x-2)² – 18 ≥ -18
Amin=-18 khi 2(x-2)²=0
x=2
b,B=9x -3x²
B= -3( x² – 3x)
B= -3(x² – 3x + 9/4 – 9/4)
B= -3(x-3/2)² + 27/4
B= 27/4 – 3(x-3/2)² ≤ 27/4
Bmax = 27/4 khi x = 3/2
c,
Ta có:
3(2² + 1)($2^{4}$ + 1)($2^{8}$ +1)($2^{16}$+1)
= (2² -1)(2²+1)($2^{4}$ + 1)($2^{8}$ +1)($2^{16}$+1)
=($2^{4}$-1 )($2^{4}$ + 1)($2^{8}$ +1)($2^{16}$+1)
=($2^{8}$ -1)($2^{8}$ +1)($2^{16}$+1)
=($2^{16}$ -1)($2^{16}$+1)
=$2^{32}$ -1