can u put this equation in function of $H$ : $T = \sqrt{h_{1}^2 - H^2}+\sqrt{h_{2}^2 -H^2}$

Question

can u put this equation in function of H :

$$T = \sqrt{h_{1}^2 - H^2}+\sqrt{h_{2}^2 -H^2}$$

to:

H = something...

$T$ and $H$ are variables, and $h_1$ and $h_2$ are constants

thank u all :D

Answer 1

$$T=\sqrt{h_1^2-H^2}+\sqrt{h_2^2-H^2}\\(T-\sqrt{h_1^2-H^2}=\sqrt{h_2^2-H^2})^2\\T^2+h_1^2-H^2-2T\sqrt{h_1^2-H^2}=h_2^2-H^2\\ T^2+h_1^2-h_2^2= +2T\sqrt{h_1^2-H^2}\\ \sqrt{h_1^2-H^2}=\frac{T^2+h_1^2-h_2^2}{2T}$$ go to the power of two again ,and find $H^2$ $$h_1^2-H^2=(\frac{T^2+h_1^2-h_2^2}{2T})^2\\ h_1^2-(\frac{T^2+h_1^2-h_2^2}{2T})^2=H^2\\\to H=\pm \sqrt {h_1^2-(\frac{T^2+h_1^2-h_2^2}{2T})^2}$$