1)Tính nhanh
(123-145)-(23+55)
(236-185)-(-85+36)
142-(150-249)-(249+42)
2) Tìm x
1)(x+3)^2=81
2)(2x-1)^4=625
3)(x-5)^4=(x-5)^6
1)Tính nhanh
(123-145)-(23+55)
(236-185)-(-85+36)
142-(150-249)-(249+42)
2) Tìm x
1)(x+3)^2=81
2)(2x-1)^4=625
3)(x-5)^4=(x-5)^6
`1)`
`1)(123-145)-(23+55)`
`=123-145-23-55`
`=(123-23)+(-145-55)`
`=100-200=-100`
`2)(236-185)-(-85+36)`
`=236-185+85-36`
`=(236-36)+(-185+85)`
`=200-100=100`
`3)142-(150-249)-(249+42)`
`=142-150+249-249-42`
`=(142-42)-150+(249-249)`
`=100-150=-50`
`2)`
` 1)(x+3)^2=81`
` (x+3)^2=9^2`
` x+3=9`
` x=6`
`2)(2x-1)^4=625`
`(2x-1)^4=5^4`
`2x-1=5`
`2x=6`
`x=3`
`3)(x-5)^4=(x-5)^6`
`(x-5)^4-(x-5)^6=0`
`(x-5)^4[1-(x-5)^2]=0`
`<=>`\(\left[ \begin{array}{l}(x-5)^4=0\\1-(x-5)^2=0\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x-5=0\\(x-5)^2=1\end{array} \right.\)
`<=>`\(\left[ \begin{array}{l}x=5\\\left[ \begin{array}{l}x-5=1\\x-5=-1\end{array} \right.⇔\left[ \begin{array}{l}x=6\\x=4\end{array} \right.\end{array} \right.\)
`=>x={4;5;6}`
1)Tính nhanh
(123-145)-(23+55)
= 123-145-23+55
=(123-123)-(145+55)
=100-200
=100+(-200)
=-100
(236-185)-(-85+36)
=236-185+85-36
=(236-36)+(-185-85)
=200-100
=100
142-(150-249)-(249+42)
=142-150+249-249-42
=(142-42)-150+(249-249)
=100-150+0
=100-150
=-50
2) Tìm x
1)(x+3)²=81
⇒(x+3)²=9²
⇒x+3 =9
⇒x =9-3
⇒x =6
Vậy x=6
2)(2x-1)^4=625
⇒(2x-1)^4=5^4
⇒(2x-1) =5
⇒2x =5-1
⇒2x =4
⇒x =4:2
⇒x =2
Vậy x=2
3)(x-5)^4=(x-5)^6
⇒(x-5)^6-(x-5)^4=0
⇒(x-5)^4.[(x-5)²-1]=0
⇒(x-5)^4=0 hoặc [(x-5)²-1]=0
TH1:
(x-5)^4=0
⇒x-5=0
⇒x =5
TH2:
[(x-5)²-1]=0
⇒(x-5)² =1
⇒(x-5)² =1 hoặc (x-5)² =-1
⇒x∈{6;4}
Vậy x∈{4;5;6}
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