5272道题目5525 条题源记录 · 相同内容已合并
根式与有理指数进阶
If \( x^n=\sqrt{2x^n+35} \) , where n is a positive integer constant, what is the value of xn?
原库参考解析
根式与有理指数挑战
\( \sqrt{k-x\ }=39-x \)
In the given equation, k is a constant. The equation has exactly one real solution. What is the minimum possible value of 4k?
原库参考解析
根式与有理指数挑战
Which expression is equivalent to \( \sqrt{x^{197}} \) , where \( x>0 \) ?
原库参考解析
根式与有理指数进阶
\( \sqrt{2x+19}=5 \)
What is the solution to the equation shown?
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根式与有理指数进阶
The function \( f \) is defined by \( f\left(x\right)=4\sqrt{x} \). For what value of x does \( f\left(x\right)=28 \)?
原库参考解析
根式与有理指数挑战
\( \sqrt{\left(x+15\right)^2}=x+15 \)
What is the least value of x that is a solution to the given equation?
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根式与有理指数进阶
The function g is defined by \( g\left(x\right)=\frac{\sqrt{cx}}{c}+17 \), where c is a negative constant. What is the value of \( g\left(25c\right) \)?
原库参考解析
根式与有理指数挑战
The function k is defined by \( k\left(s\right)=\sqrt{s+110} \). If \( k\left(53p\right)=p \), where p is a constant, what is the value of p?
原库参考解析
根式与有理指数挑战
If n and k are numbers greater than 1 and \( \sqrt[4]{n^{5}} \) is equivalent to \( \sqrt[5]{k^{2}} \), for what value of a is \( n^{2a+1} \) equal to k?
原库参考解析
根式与有理指数进阶
Which expression is equivalent to\( \left(x\right)^{\frac{1}{17}} \), where \( x>0 \)?
原库参考解析
根式与有理指数挑战
\( r=\sqrt{9w-5} \)
The given equation relates the real numbers r and w, where \( w>\frac{5}{9} \).Which equation correctly expresses w in terms of r ?
原库参考解析
根式与有理指数挑战
For a certain circuit, its power \( P \), in watts, current \( C \), in amperes; voltage \( V \), in volts; and resistance \( R \), in ohms, are related as \( \frac{CV^2}{P}=\sqrt{PR} \), where \( P \), \( C \), \( V \), and \( R \) are positive. When \( R=18 \), which equation correctly expresses \( P \) in terms of \( C \) and \( V \)?
原库参考解析
