Tìm số tự nhiên x, biết 79,86 < x < 80,15
A . 78 B .79 C . 80 D . 81
Giải nhanh giúp mình với
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a) Đặt: \(x+13=a^2,x-2=b^2\)
\(\Rightarrow a^2-b^2=15\Leftrightarrow\left(a-b\right)\left(a+b\right)=15\Rightarrow\orbr{\begin{cases}a-b=1,a+b=15\\a-b=3,a+b=5\end{cases}}\)
\(\Leftrightarrow\orbr{\begin{cases}a=8,b=7\Rightarrow x=51\\a=4,b=1\Rightarrow x=3\end{cases}}\)
b) Đặt \(x^2+6x+16=n^2\Leftrightarrow n^2-\left(x+3\right)^2=7\Leftrightarrow\left(n-x-3\right)\left(n+x+3\right)=7\)
\(\Leftrightarrow\hept{\begin{cases}n-x-3=1\\n+x+3=7\end{cases}\Leftrightarrow}\hept{\begin{cases}x=0\\n=4\end{cases}\Rightarrow x=0}\)
c) \(x^2+3x+9\)là số chính phương \(\Leftrightarrow4\left(x^2+3x+9\right)\)là số chính phương
Đặt \(4\left(x^2+3x+9\right)=m^2\Leftrightarrow m^2-\left(2x+3\right)=27\Leftrightarrow\left(m-2x-3\right)\left(m+2x+3\right)=27\)
\(\Rightarrow\orbr{\begin{cases}m-2x-3=1,m+2x+3=27\\m-2x-3=3,m+2x+3=9\end{cases}\Leftrightarrow\orbr{\begin{cases}m=14,x=5\\m=6,x=0\end{cases}}}\)
d) Đặt \(x+26=k^3,x-11=l^3\)
\(\Rightarrow k^3-l^3=37\Leftrightarrow\left(k-l\right)\left(k^2+l^2+kl\right)=37\Rightarrow\orbr{\begin{cases}k-l=1\\k^2+l^2+kl=37\end{cases}}\)
\(\Rightarrow k=4,l=3\Rightarrow x=38\)
\(x\left(x+1\right)=156\)
\(\Rightarrow x^2+x=156\)
\(\Rightarrow x^2+x-156=0\)
\(\Rightarrow x^2+13x-12x-156=0\)
\(\Rightarrow x\left(x+13\right)-12\left(x+13\right)=0\)
\(\Rightarrow\left(x+13\right)\left(x-12\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=12\\x=-13\end{matrix}\right.\)
___________________
\(x\left(x+1\right)=342\)
\(\Rightarrow x^2+x=342\)
\(\Rightarrow x^2+x-342=0\)
\(\Rightarrow x^2+19x-18x-342=0\)
\(\Rightarrow x\left(x+19\right)-18\left(x+19\right)=0\)
\(\Rightarrow\left(x+19\right)\left(x-18\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-19\\x=18\end{matrix}\right.\)
__________________
\(x\left(x+1\right)=650\)
\(\Rightarrow x^2+x=650\)
\(\Rightarrow x^2-x+650=0\)
\(\Rightarrow x^2+26x-25x-650=0\)
\(\Rightarrow x\left(x+26\right)-25\left(x+26\right)=0\)
\(\Rightarrow\left(x+26\right)\left(x-25\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-26\\x=25\end{matrix}\right.\)
______________________
\(x\left(x+1\right)=380\)
\(\Rightarrow x^2+x=380\)
\(\Rightarrow x^2+x-380=0\)
\(\Rightarrow x^2+20x-19x-380=0\)
\(\Rightarrow x\left(x+20\right)-19\left(x+20\right)=0\)
\(\Rightarrow\left(x+20\right)\left(x-19\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-20\\x=19\end{matrix}\right.\)
a, \(x\).(\(x\) + 1) = 156
156 = 22.3.13 = 12.13
Vậy \(x\).(\(x\) + 1) = 12.13
Vậy \(x\) = 12
b, \(x.\)(\(x\) + 1) = 342
342 = 2.32.19 = 18.19
\(x\).(\(x+1\)) = 18.19
\(x\) = 18
c, \(x\).(\(x\) + 1) = 650
650 = 2.52.13 = 25.26
\(x\).(\(x\) +1) = 25.26
\(x\) = 25
d, \(x\).(\(x\) +1) = 380
380 = 22.5.19 = 19.20
\(x\).(\(x\) + 1) = 19.20
\(x\) = 19
a) x3 = 8
=> x3 = 23
=> x = 2
Vậy x = 2
b) 3x = 81
=> 3x = 34
=> x = 4
Vậy x = 4
c) x3 = x
=> x3 - x = 0
=> x.(x2 - 1) = 0
=> x.(x - 1).(x + 1) = 0
=> \(\left[\begin{array}{nghiempt}x=0\\x-1=0\\x+1=0\end{array}\right.\) => \(\left[\begin{array}{nghiempt}x=0\\x=1\\x=-1\end{array}\right.\)
Vậy \(x\in\left\{0;1;-1\right\}\)
d) 2x2 = 6x
=> 2x2 - 6x = 0
=> 2x.(x - 3) = 0
=> x.(x - 3) = 0
=> \(\left[\begin{array}{nghiempt}x=0\\x-3=0\end{array}\right.\)=> \(\left[\begin{array}{nghiempt}x=0\\x=3\end{array}\right.\)
Vậy \(x\in\left\{0;3\right\}\)
a) (x- 2)2 =25
(x- 2)2 =52
\(\Rightarrow\orbr{\begin{cases}x-2=5\\x-2=-5\end{cases}\Rightarrow\orbr{\begin{cases}z=7\\x=-3.\end{cases}}}\)
Vậy..............................................
b) (3x-6).3=34
3x-6=34:3
3x-6=9
3x=9+6
3x=15
x=15:3
x=5
Vậy x=5
a)(x-2)\(^2\)=25
\(\rightarrow\)(x-2)\(^2\)=5\(^2\)
\(\rightarrow\)x-2=5 hoặc x-2=(-5)
TH1:x-2=5 TH2:x-2=(-5)
\(\rightarrow\)x=5+2 \(\rightarrow\)x=(-5)+2
\(\rightarrow\)x=7 \(\rightarrow\)x=(-3)
Vậy x =7;x=(-3)
b)(3x-6).3=3\(^4\)
\(\rightarrow\)(3x-6).3=81
\(\rightarrow\)(3x-6) =81:3
\(\rightarrow\)3x-6 =27
\(\rightarrow\)3x =27+6
\(\rightarrow\)3x =33
\(\rightarrow\)x =33:3
\(\rightarrow\)x =11
Vậy x=11
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