tìm x thuộc N biết
a)\(1^3\)+\(2^3\)+\(3^3\)+.......+\(10^3\)=\(\left(x+1^{ }^{ }\right)^2\)
b)1+3+5+.......+99=\(\left(x-2^{ }\right)^2\)
giúp mình nha
K
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H
26 tháng 12 2022
\(B1\\ a,2x+10y=2\left(x+5y\right)\\ b,x^2+4x+4=x^2+2.2x+2^2=\left(x+2\right)^2\\ c,x^2-y^2+10y-25\\ =\left(x^2-y^2\right)+5\left(2y-5\right)\\ =\left(x-y\right)\left(x+y\right)+5\left(2y-5\right)\\ B2\)
\(a,x^2-3x+x-3=0\\ =>x\left(x-3\right)+\left(x-3\right)=0\\ =>\left(x+1\right)\left(x-3\right)=0\\ =>\left[{}\begin{matrix}x+1=0\\x-3=0\end{matrix}\right.=>\left[{}\begin{matrix}x=-1\\x=3\end{matrix}\right.\\ b,2x\left(x-3\right)-\dfrac{1}{2}\left(4x^2-3\right)=0\\ =>2x^2-6x-2x^2+\dfrac{3}{2}=0\\ =>-6x=-\dfrac{3}{2}\\ =>x=\left(-\dfrac{3}{2}\right):\left(-6\right)\\ =>x=\dfrac{1}{4}\\ c,x^2-\left(x-3\right)\left(2x-5\right)=9\\ =>x^2-2x^2+6x+5x-15=9\\ =>-x^2+11-15-9=0\\ =>-x^2+11x-24=0\\ =>-x^2+8x+3x-24=0\\ =>-x\left(x-8\right)+3\left(x-8\right)=0\\ =>\left(3-x\right)\left(x-8\right)=0\\ =>\left[{}\begin{matrix}3-x=0\\x-8=0\end{matrix}\right.=>\left[{}\begin{matrix}x=3\\x=8\end{matrix}\right.\)
14 tháng 11 2023
1: ĐKXĐ: x+3>=0
=>x>=-3
\(\sqrt{x+3}>2\)
=>x+3>4
=>x>4-3=1
2: ĐKXĐ: \(\left\{{}\begin{matrix}x>=0\\x< >4\end{matrix}\right.\)
\(\dfrac{\sqrt{x}+1}{\sqrt{x}-2}< 1\)
=>\(\dfrac{\sqrt{x}+1}{\sqrt{x}-2}-1< 0\)
=>\(\dfrac{\sqrt{x}+1-\sqrt{x}+2}{\sqrt{x}-2}< 0\)
=>\(\dfrac{3}{\sqrt{x}-2}< 0\)
=>\(\sqrt{x}-2< 0\)
=>\(\sqrt{x}< 2\)
=>0<=x<4
3: ĐKXĐ: x>=0
\(\left(\sqrt{x}-1\right)\left(\sqrt{x}-3\right)-5=\sqrt{x}\left(\sqrt{x}+2\right)-5\)
=>\(x-4\sqrt{x}+3-5=x+2\sqrt{x}-5\)
=>\(x-4\sqrt{x}-2-x-2\sqrt{x}+5=0\)
=>\(-6\sqrt{x}+3=0\)
=>\(-6\sqrt{x}=-3\)
=>\(\sqrt{x}=\dfrac{1}{2}\)
=>x=1/4(nhận)
15 tháng 10 2023
a: 78x(x-97)-x+97=0
=>(x-97)(78x-1)=0
=>\(\left[{}\begin{matrix}x=97\\x=\dfrac{1}{78}\end{matrix}\right.\)
b: \(\dfrac{2}{3}x\left(x^2-4\right)=0\)
=>\(x\left(x-2\right)\left(x+2\right)=0\)
=>\(\left[{}\begin{matrix}x=0\\x=2\\x=-2\end{matrix}\right.\)
c: \(\left(x+2\right)^2-\left(x-2\right)\left(x+2\right)=0\)
=>\(x^2+4x+4-x^2+4=0\)
=>4x+8=0
=>x+2=0
=>x=-2
T
15 tháng 10 2023
\(a,78x\left(x-97\right)-x+97=0\)
\(\Leftrightarrow78x\left(x-97\right)-\left(x-97\right)=0\)
\(\Leftrightarrow\left(x-97\right)\left(78x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x-97=0\\78x-1=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=97\\x=\dfrac{1}{78}\end{matrix}\right.\)
\(b,\dfrac{2}{3}x\left(x^2-4\right)=0\)
\(\Leftrightarrow\dfrac{2}{3}x\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}\dfrac{2}{3}x=0\\x-2=0\\x+2=0\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\\x=-2\end{matrix}\right.\)
\(c,\left(x+2\right)^2-\left(x-2\right)\left(x+2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\left[\left(x+2\right)-\left(x-2\right)\right]=0\)
\(\Leftrightarrow\left(x+2\right)\left(x+2-x+2\right)=0\)
\(\Leftrightarrow\left(x+2\right)\cdot4=0\)
\(\Leftrightarrow x+2=0\)
\(\Leftrightarrow x=-2\)
27 tháng 6 2023
2:
a: A(x)=0
=>5x-10-2x-6=0
=>3x-16=0
=>x=16/3
b: B(x)=0
=>5x^2-125=0
=>x^2-25=0
=>x=5 hoặc x=-5
c: C(x)=0
=>2x^2-x-3=0
=>2x^2-3x+2x-3=0
=>(2x-3)(x+1)=0
=>x=3/2 hoặc x=-1
YP
1
21 tháng 11 2021
\(\left(-\dfrac{3}{4}x+1\right)\div\dfrac{2}{3}=1\)
\(-\dfrac{3}{4}x+1=1\times\dfrac{2}{3}\)
\(-\dfrac{3}{4}x+1=\dfrac{2}{3}\)
\(-\dfrac{3}{4}x=\dfrac{2}{3}-1\)
\(-\dfrac{3}{4}x=-\dfrac{1}{3}\)
\(x=-\dfrac{1}{3}\div\left(-\dfrac{3}{4}\right)\)
\(x=\dfrac{4}{9}\)
x+3=6
x=6-3
x=3
KK
5 tháng 9 2021
a. (x - 22) - 1 = 0
<=> x - 4 - 1 = 0
<=> x = 5
b. 4 - (x - 2)2 = 0
<=> 22 - (x - 2)2 = 0
<=> (2 - x + 2)(2 + x - 2) = 0
<=> x(4 - x) = 0
<=> \(\left[{}\begin{matrix}x=0\\4-x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\end{matrix}\right.\)
KK
5 tháng 9 2021
d. (3x - 2)2 - (2x + 3)2 = 5(x + 4)(x - 4)
<=> (3x - 2 - 2x - 3)(3x - 2 + 2x + 3) = 5(x2 - 16)
<=> (x - 5)(5x + 1) = 5x2 - 80
<=> 5x2 + x - 25x - 5 = 5x2 - 80
<=> 5x2 - 5x2 + x - 25x = -80 + 5
<=> -24x = -75
<=> x = \(\dfrac{25}{8}\)
10 tháng 1
a: \(\left(2^3\right)^{1^{2005}}\cdot x+2005^0\cdot x=9915:3+1^{2025}\)
=>\(8\cdot x+1\cdot x=3305+1\)
=>\(9x=3306\)
=>\(x=\dfrac{3306}{9}=\dfrac{1102}{3}\)
b: \(2^x+2^{x+1}+2^{x+2}+2^{x+3}=480\)
=>\(2^x+2^x\cdot2+2^x\cdot4+2^x\cdot8=480\)
=>\(2^x\left(1+2+4+8\right)=480\)
=>\(2^x\cdot15=480\)
=>\(2^x=32\)
=>\(2^x=2^5\)
=>x+5
b) 50(1+99) = (x-2)2
502 = (x-2)2
x-2 = 50
x = 52
a) (\(\frac{10\left(10+1\right)}{2}\))2 = (x+1)2
552 = (x+1)2
55 =x+1
x = 54
xem đi, mk làm tip cau b