If \(\dfrac{x}{x+1}+\dfrac{x+1}{x} = \dfrac52\), then find x.
1 or -2
Let \(u = \dfrac{x}{x+1}\), so the equation becomes \(u+\dfrac1u = \dfrac52\).
\(2u^2-5u+2=0 \Rightarrow u = 2\ \text{or}\ u=\dfrac12\).
If \(u=2\): \(\dfrac{x}{x+1}=2 \Rightarrow x=2x+2 \Rightarrow x=-2\).
If \(u=\tfrac12\): \(\dfrac{x}{x+1}=\tfrac12 \Rightarrow 2x=x+1 \Rightarrow x=1\).
Hence, the values of x are 1 or -2.
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Important Questions from Algebric Equations
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
If m + n = 24, then (m - 16)³ + (n - 8)³ is ____.
For the following equations, what are the values of a and b to have infinitely many solutions?
ax + by = 2
3x - (5 - 2ay) = 6
Simplify the following expression:
\(\frac{(x - y)^3 + (y - z)^3 + (z - x)^3}{(x - y)(y - z)(z - x)}\)
