Answer:
Explanation:
The equations you provided, T=(H−G)/S, S=(G−H)/T, and H=(G−T)/S, are equivalent to the equation G=H−T×S. These equations describe a system in which the variables G, H, S, and T are related in a certain way.
T=(H−G)/S means that T is equal to the ratio of (H−G) divided by S. Similarly, S=(G−H)/T means that S is equal to the ratio of (H−G) divided by T. And H=(G−T)/S means that H is equal to the ratio of (G−T) divided by S. These equations can be used to solve for the values of T, S, and H in terms of G, or vice versa, depending on the values of the variables that are given.
To solve for G in terms of T, S, and H, we can start by rewriting the equations in terms of G:
G=(H−T)/S or S=(G−H)/T or H=(G−T)/S
Next, we eliminate G from the equations by multiplying the second and third equations:
S=(G−H)/T × (T−H)/S = (G−H)(T−H)/S^2
Simplifying, we get:
(G−H)T = S^2(T−H)
Solving for G, we get:
G=(S^2(T−H)+HT)/(S(H−T))
To solve for H in terms of T, S, and G, we can use the same approach:
H=(G−T)/S or S=(G−H)/T or T=(G−H)/S
Next, we eliminate G by multiplying the first and third equations:
H=(G−T)/S × (T−H)/S = (G−T)(T−H)/S^2
Simplifying, we get:
(G−H)T = H^2(S^2−T^2)
Solving for H, we get:
H=(S^2(G−T) ± sqrt(S^4(G−T)^