1 Tính nhanh a) 29,9 . 30,1 b) (31,8) ² – 63,6 .21,8 + (21,8) ² 2 Tìm x a) ( x-3) ² -4 = 0 b) x ² – 2x = 24 15/07/2021 Bởi Josie 1 Tính nhanh a) 29,9 . 30,1 b) (31,8) ² – 63,6 .21,8 + (21,8) ² 2 Tìm x a) ( x-3) ² -4 = 0 b) x ² – 2x = 24
Đáp án: $1.$ $a, 29,9 . 30,1 $ $= (30 – 0,1)(30 + 0 ,1)$ $= 30² – 0,1²$ $= 900 – 0,01$ $= 899,99 $ $b,(31,8)² – 63,6 . 21,8 + (21,8)² $ $= (31,8)² – 2 . 31,8 . 21,8 + (21,8)² $$= (31,8 – 21,8)² $ $= 10²$ $= 100 $ $2.$ $a, (x – 3)² – 4 = 0$ $⇔ (x – 3)² – 2² = 0$ $⇔ (x – 3 – 2)(x – 3 + 2) = 0$ $⇔ (x – 5)(x – 1) = 0$ $⇔$ \(\left[ \begin{array}{l}x-5=0\\x-1=0\end{array} \right.\) $⇔$ \(\left[ \begin{array}{l}x=5\\x=1\end{array} \right.\) $b, x² – 2x = 24 $ $⇔ x² – 2x + 1 – 25 = 0 $ $⇔ (x – 1)² – 5² = 0 $ $⇔ (x – 1 – 5)(x – 1 + 5) = 0 $ $⇔ (x – 6)(x + 4) = 0 $ $⇔$ \(\left[ \begin{array}{l}x-6=0\\x+4=0\end{array} \right.\) $⇔$ \(\left[ \begin{array}{l}x=6\\x=-4\end{array} \right.\) Bình luận
Giải thích các bước giải: 1.a) `29,9.30,1` `=(30-0,1)(30+0,1)` `=30^2-0,1^2` `=900-0,01=899,99` b) `31,8^2-63,6.21,8+21,8^2` `=(31,8-21,8)^2` `=10^2=100` 2.a) `(x-3)^2-4=0` `=>(x-3-2)(x-3+2)=0` `=>(x-5)(x-1)=0` `=>`\(\left[ \begin{array}{l}x-5=0\\x-1=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=5\\x=1\end{array} \right.\) b) `x^2-2x=24` `=>(x^2-2x+1)=25` `=>(x-1)^2-25=0` `=>(x-1-5)(x-1+5)=0` `=>(x-6)(x+4)=0` `=>`\(\left[ \begin{array}{l}x-6=0\\x+4=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=6\\x=-4\end{array} \right.\) Bình luận
Đáp án:
$1.$
$a, 29,9 . 30,1 $
$= (30 – 0,1)(30 + 0 ,1)$
$= 30² – 0,1²$
$= 900 – 0,01$
$= 899,99 $
$b,(31,8)² – 63,6 . 21,8 + (21,8)² $
$= (31,8)² – 2 . 31,8 . 21,8 + (21,8)² $
$= (31,8 – 21,8)² $
$= 10²$
$= 100 $
$2.$
$a, (x – 3)² – 4 = 0$
$⇔ (x – 3)² – 2² = 0$
$⇔ (x – 3 – 2)(x – 3 + 2) = 0$
$⇔ (x – 5)(x – 1) = 0$
$⇔$ \(\left[ \begin{array}{l}x-5=0\\x-1=0\end{array} \right.\)
$⇔$ \(\left[ \begin{array}{l}x=5\\x=1\end{array} \right.\)
$b, x² – 2x = 24 $
$⇔ x² – 2x + 1 – 25 = 0 $
$⇔ (x – 1)² – 5² = 0 $
$⇔ (x – 1 – 5)(x – 1 + 5) = 0 $
$⇔ (x – 6)(x + 4) = 0 $
$⇔$ \(\left[ \begin{array}{l}x-6=0\\x+4=0\end{array} \right.\)
$⇔$ \(\left[ \begin{array}{l}x=6\\x=-4\end{array} \right.\)
Giải thích các bước giải:
1.a) `29,9.30,1`
`=(30-0,1)(30+0,1)`
`=30^2-0,1^2`
`=900-0,01=899,99`
b) `31,8^2-63,6.21,8+21,8^2`
`=(31,8-21,8)^2`
`=10^2=100`
2.a) `(x-3)^2-4=0`
`=>(x-3-2)(x-3+2)=0`
`=>(x-5)(x-1)=0`
`=>`\(\left[ \begin{array}{l}x-5=0\\x-1=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=5\\x=1\end{array} \right.\)
b) `x^2-2x=24`
`=>(x^2-2x+1)=25`
`=>(x-1)^2-25=0`
`=>(x-1-5)(x-1+5)=0`
`=>(x-6)(x+4)=0`
`=>`\(\left[ \begin{array}{l}x-6=0\\x+4=0\end{array} \right.\) `=>`\(\left[ \begin{array}{l}x=6\\x=-4\end{array} \right.\)