I Trouble Solving an Equation that has square roots on both sides

  • I
  • Thread starter Thread starter thatboi
  • Start date Start date
  • Tags Tags
    Roots Square
AI Thread Summary
To solve the equation A(-√(C²+4F₊) - C) = B(√(C²+4F₋) + C), the challenge lies in eliminating the square roots from both sides. The discussion reveals that by manipulating the equation and squaring both sides, one can simplify the problem, although it introduces additional complexity due to constants. The resulting polynomial form, αC⁴ + βC² + γ = 0, indicates that it can be approached using methods for solving quartic equations. Participants note that while the equation is complex, it remains solvable with careful algebraic manipulation. Overall, the equation presents a challenging but manageable problem for those familiar with polynomial equations.
thatboi
Messages
130
Reaction score
20
Hey all,
I am having trouble solving the following equation for C
$$A(-\sqrt{C^2+4F_{+}}-C) = B(\sqrt{C^2+4F_{-}}+C)$$
I don't know how to get ride of the square roots on both sides.
Any help would be appreciated, thanks!
 
Mathematics news on Phys.org
\begin{align*}
\sqrt{C^2+4F_{+}}&=D\sqrt{C^2+4F_{-}}+EC\\
C^2+4F_{+}&=D^2\left(C^2+4F_{-}\right)+E^2C^2+2DEC\sqrt{C^2+4F_{-}}\\
GC^2+H&=C\sqrt{C^2+4F_{-}}\\
G^2C^4+H^2+2GHC^2&=C^2(C^2+4F_{-})\\
\alpha C^4 + \beta C^2 +\gamma &=0
\end{align*}

Looks like some work to do because of the many constants, but doable.
 
  • Like
  • Informative
Likes topsquark, bob012345, thatboi and 1 other person
Suppose ,instead of the usual x,y coordinate system with an I basis vector along the x -axis and a corresponding j basis vector along the y-axis we instead have a different pair of basis vectors ,call them e and f along their respective axes. I have seen that this is an important subject in maths My question is what physical applications does such a model apply to? I am asking here because I have devoted quite a lot of time in the past to understanding convectors and the dual...
Fermat's Last Theorem has long been one of the most famous mathematical problems, and is now one of the most famous theorems. It simply states that the equation $$ a^n+b^n=c^n $$ has no solutions with positive integers if ##n>2.## It was named after Pierre de Fermat (1607-1665). The problem itself stems from the book Arithmetica by Diophantus of Alexandria. It gained popularity because Fermat noted in his copy "Cubum autem in duos cubos, aut quadratoquadratum in duos quadratoquadratos, et...
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. In Dirac’s Principles of Quantum Mechanics published in 1930 he introduced a “convenient notation” he referred to as a “delta function” which he treated as a continuum analog to the discrete Kronecker delta. The Kronecker delta is simply the indexed components of the identity operator in matrix algebra Source: https://www.physicsforums.com/insights/what-exactly-is-diracs-delta-function/ by...

Similar threads

Replies
19
Views
3K
Replies
10
Views
989
Replies
22
Views
2K
Replies
6
Views
3K
Replies
13
Views
2K
Replies
2
Views
2K
Back
Top