![Solutions of $\sqrt{x^2+5x-14} + |x^2+4x-12|=0$ [duplicate]](https://news.conceivablytech.com/uploads/solutions-of-sqrt-x-2-5x-14-x-2-4x-12-0-duplicate_720.jpg)
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Solutions of $\sqrt{x^2+5x-14} + |x^2+4x-12|=0$ [duplicate]
My attempt: Given, $$\sqrt{x^2+5x-14} + |x^2+4x-12|=0 \tag{1}$$ Since $|a|=\sqrt{a^2}$, $$\sqrt{x^2+5x-14}=-\sqrt{(x^2+4x-12)^2}$$ Squaring both sides, $$...
Apr 16, 2026
Archive: Updates
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Combinations and Probability with keyboards
I have the question Computer keyboard failures can be attributed to electrical defects or mechanical defects. A repair facility currently has 25 failed ke...
Apr 16, 2026
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Fundamental solution of heat equation with time dependent diffusion coefficient
Consider the heat equation $$ u_{t} = k(t) \Delta u + f(t,x),~~x \in \mathbb{R}^{n},t>0 $$ $$ u(0,x) = u_{0}(x). $$ If $k(t) = k$, then $$ u(t,x) = \in...
Apr 16, 2026
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Find an unit vector parallel to the line $y=7x-3$
I know that the magnitude of a unit vector is $1$, and in order for two vectors to be parallel the angle between them should be $0^\circ$ or $180^\circ$. ...
Apr 16, 2026
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Why is $\sin(\pi/6) = 0.5$?
Why is $\sin(30^\circ)$ exactly $0.5,$ when it could be 0.49999 or something else? There must be an easy geometric explanation?
Apr 16, 2026
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What is the name of the approximation $ \left(1-\frac{1}{x}\right)^n \approx e^{-n/x} $?
Which approximation allows for the following? $$ \left(1-\frac{1}{x}\right)^n \approx e^{-n/x} $$ Here both $x$ and $n$ are variables.
Apr 16, 2026
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How to derive the equilibrium length of a spring?
A straight wire rotates with constant angular speed $\omega$ about one of its end points (the origin $O$) in a horizontal plane containing $e_1$ and $e_2$...
Apr 16, 2026
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$x$ and $y$-intercepts of an absolute value function $f(x)=-3|x-2|-1$
I am to find the $x$ and $y$-intercepts of the function $$f(x)=-3|x-2|-1.$$ The solution is provided in my book as $(0, -7)$; no $x$ intercepts. I cannot ...
Apr 16, 2026
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Can $X \times Y = \overline{XY}$?
Is it possible that $XY = \overline{XY}$, where $\overline{XY} = 10X+Y$, $X \in \{1,\dots,9\}$ and $Y = \{0,\dots,9\}$? I am trying to show there is no wa...
Apr 16, 2026
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Difference Between Cantor's Ordinals and Von Neumann Ordinals?
Cantor's Naive Set Theory allows the construction of the set of all ordinals, which contains itself, which triggers the Burali-Forti Paradox. ZFC bot...
Apr 16, 2026
