Find the integer solution of the equation \(x^2+xy+y^2=x^2y^2\)
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find the value of b and c for a quadratic function f(x) = x2+bx+c such that the solution of the equation f(x)=0 are \(\sqrt{3},-\sqrt{3}\)
Given the equation (x - m)(m - 1) + (x - 1)(m + 1) = -2m. Find all values of m such that this equation has no solution. Answer: m = ...........
A solution to the equation (x+a)(x+b)(x+c)+5=0 is x=1 where a,b,c are differents integers Find the value of a+b+c
Thay x=1 vào pt, ta có: \(\left(a+1\right)\left(b+1\right)\left(c+1\right)=-5\left(1\right)\)
vì vai trò của a,b,c là như nhau, giả sử:\(a>b>c\Rightarrow a+1>b+1>c+1\left(2\right)\)
vì a,b,c là số nguyên nên a+1,b+1,c+1 cũng là số nguyên (3)
từ (1),(2),(3)\(\Rightarrow\hept{\begin{cases}a+1=5\\b+1=1\\c+1=-1\end{cases}\Leftrightarrow\hept{\begin{cases}a=4\\b=0\\c=-2\end{cases}}}\)
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Find all pairs of positive integers (x;y) satisfy the equation: 1!+2!+3!+.......x!=y2
1. Determine all pairs of integer (x;y) such that 2xy^2+x+y+1x^2+2y^2+xy 2. Let a,b,c satisfies the conditions hept{begin{cases}5ge age bge cge0a+ble8a+b+c10end{cases}} Prove that 2a^2+b^2+c^2le38 3. Let a nad b satis fy the conditions hept{begin{cases}a^3-6a^2+15a9b^3-3b^2+6b-1end{cases}} Find the value ofleft(a-bright)^{2014} ? 4. Find the smallest positive integer n such that the number 2^n+2^8+2^{11} is a perfect square.
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1. Determine all pairs of integer (x;y) such that \(2xy^2+x+y+1=x^2+2y^2+xy\)
2. Let a,b,c satisfies the conditions
\(\hept{\begin{cases}5\ge a\ge b\ge c\ge0\\a+b\le8\\a+b+c=10\end{cases}}\)
Prove that \(2a^2+b^2+c^2\le38\)
3. Let a nad b satis fy the conditions
\(\hept{\begin{cases}a^3-6a^2+15a=9\\b^3-3b^2+6b=-1\end{cases}}\)
Find the value of\(\left(a-b\right)^{2014}\) ?
4. Find the smallest positive integer n such that the number \(2^n+2^8+2^{11}\) is a perfect square.
a) (x2y2 – xy + 2y)(x – 2y); b) (x2 – xy + y2)(x + y).
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a) (x2y2 – xy + 2y)(x – 2y); b) (x2 – xy + y2)(x + y).
Given the equation (x - m)(m - 1) + (x - 1)(m + 1) = -2m.
Find all values of m such that this equation has no solution.
Answer: m = ...........
mọi người giúp minh nhé mình đang cần gấp Thanks trc
1.If 2x-y5 then the value of Mleft(x+2y-3right)^2-left(6x+2yright)left(x+2y-3right)+9x^2+6xy+y^22.The free coefficient in the following poly nomaial: left(2x-2right)left(x+1right)left(7-x^2right)is:3.The greatest integer number x such that frac{2x-1}{x-3}-1 0 is:4.How many of the integer n such that satisfy the inequality left(n-3right)^2-left(n-4right)left(n+4right) 43 are less than 3?5.The opposite fraction of frac{x-2}{7-x} is:
Đọc tiếp
1.If 2x-y=5 then the value of M=\(\left(x+2y-3\right)^2-\left(6x+2y\right)\left(x+2y-3\right)+9x^2+6xy\)
\(+y^2\)
2.The free coefficient in the following poly nomaial: \(\left(2x-2\right)\left(x+1\right)\left(7-x^2\right)is:\)
3.The greatest integer number x such that \(\frac{2x-1}{x-3}-1< 0\) is:
4.How many of the integer n such that satisfy the inequality \(\left(n-3\right)^2-\left(n-4\right)\left(n+4\right)< =43\) are less than 3?
5.The opposite fraction of \(\frac{x-2}{7-x}\) is:
How many ordered pái of interger (x;y) that satisfy the equation \(2x^2+y^2+xy=2\left(x+y\right)\)
4x2+y2+2xy=4x+4y
=>(x2+2xy+y2)+3x2+y2-4x-4y=0
=> (x+y)2+3\(\left(x^2-\dfrac{4}{3}x\right)+\left(y^2-4y\right)=0\)
=> (x+y)2+3\(\left(x^2-2.\dfrac{4}{6}+\dfrac{16}{36}-\dfrac{16}{36}\right)+\left(y^2-4y+4\right)-4=0\)
=> (x+y)2+3\(\left(x-\dfrac{4}{6}\right)^2-\dfrac{4}{3}+\left(y-2\right)^2-4=0\)
=> (x+y)2+3\(\left(x-\dfrac{4}{6}\right)^2+\left(y-2\right)^2=\dfrac{16}{3}\)
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