5272道题目5525 条题源记录 · 相同内容已合并
二次方程・零点与韦达定理进阶
\( x^2=\left(40\right)\left(40\right) \)
What is the positive solution to the given equation?
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二次方程・零点与韦达定理进阶
\( y=4x+12 \)
\( y=\left(x+2\right)^2 \)
A solution to the given system of equations is (x, y). What is the value of \( x^2 \)?
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二次方程・零点与韦达定理挑战
\( \frac{4}{9}\left(4x+9\right)\left(x+\sqrt{4k+9}\right)\left(x-\sqrt{4k+9}\right)=0 \)
In the given equation, k is a positive constant. The product of the solutions to the equation is 81. What is the value of k?
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二次方程・零点与韦达定理挑战
\( 4x^2+5x-5=0 \)
What is the greatest solution to the given equation?
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二次方程・零点与韦达定理挑战
\( 21x^2+\left(21s+r\right)x+rs=0 \)
In the given equation, r and s are positive constants. The product of the solutions to the given equation is krs, where k is a constant. What is the value of k?
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二次方程・零点与韦达定理挑战
\( -8x\left(x+9\right)=40 \)
One solution to the given equation can be written as \( x=-\frac{s+\sqrt{t}}{2} \), where s and t are positive integers. What is the value of \( \frac{s}{t} \)?
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二次方程・零点与韦达定理挑战
\( \left(x-k\right)^2=\left(k-4a\right)\left(x-k\right) \)
In the given equation, a and k are constants, where \( k>4a \). The sum of the solutions to the equation is \( 3k+35 \). What is the value of a?
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二次方程・零点与韦达定理挑战
\( \frac{5}{8}\left(5x+8\right)\left(x+\sqrt{5k+8}\right)\left(x-\sqrt{5k+8}\right) \) =0
In the given equation, k is a positive constant. The product of the solutions to the equation is 64. what is the value of k?
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二次方程・零点与韦达定理挑战
\( x^2+9x+6=0 \)
One solution to the given equation can be written as\( x=\frac{-9+\sqrt{k}}{2} \) , where k is a constant. What is the value of k?
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二次方程・零点与韦达定理挑战
The function f is defined by\( f\left(x\right)=ax^2+bx+c \) , where a, b, and c are constant and l < a < 4. The graph of y = f (x) in the xy-plane passes through the points (12, 0) and (-6, 0). If a is an integer, what could be the value of a + b?
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二次方程・零点与韦达定理进阶
x + y = 7
2x2 + 2xy = 42
Which ordered pair (x, y) is the solution to the given system of equations?
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二次方程・零点与韦达定理进阶
If x < 0, what value of x will satisfy the equation 3x2 − 2 = −5x ?
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