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Clear["`*"] eqns1 = {x^2/2^2 + y^2/1^2 == 1, y == x + 1}; SolveValues[eqns1, {x, y}] {{x1, y1}, {x2, y2}} = Sort[%, #1[[1]] < #2[[1]] &] this is method one A friend has provided me with several …

method two: ClearAll[Evaluate[Context[] <> "*"]] eqns1 = {x^2 - y == 0, y == x + 1}; {{x1, y1}, {x2, y2}} = SolveValues[eqns1, {x, y}] {y1, y2} {y1, y2} = {Min@%, Max@%}

ClearAll[Evaluate[Context[] <> "*"]] eqns1 = {x^2 - y == 0, y == x + 1}; {{x1, y1}, {x2, y2}} = SolveValues[eqns1, {x, y}] The above equations have two sets of solutions. How to compare the size of …

There is an equation: (-3 + 4 k^2)/(-6 + m^2) == 1 and a fraction: Sqrt[m^2]/Sqrt[1 + k^2] How can the equation be used to replace m ^ 2 in the fraction? The expected result is: Sqrt[4 k^2 + 3]/Sqr …

The operation rules are as follows：The coefficients in the equation are not equal to zero，That is to say, in the process of converting to an integral equation, if a common factor is proposed and the r …

There is an equation : -2 == Sqrt[x^2 + (-2 - y)^2] - Sqrt[x^2 + (2 - y)^2] There are two radicals on the right side of equal to coincidence，The following are about six steps of our manual calculatio …

Why is there no solution for the system of equations with a greater than 0? Solve[{c^2 - b^4/a^2 == 0, a^2 + b^2 == c^2, e == c/a, a > 0, e > 1}, e, {a, c}] Why can we solve the value of e by sett …

The given equation is: y^2 (1 - λ^2) + a^2 λ^2 (-1 - (λ^2 (1 - λ^2))/(-1 + \ λ^2)^2) + (1 - λ^2) (x - ( a λ^2)/(-1 + λ^2))^2 == 0 Note that this type of equation is in the form of a circle, s …

The elliptic trajectory equation and hyperbola trajectory equation are generated according to the code, but the final form is not the standard form. How to generate the standard equation form? The sta …

How to optimize the code for deriving the standard equation of the Apollonian circle? Based on xzczd's solution therein: ClearAll["`*"] eq = 25 x^2 - 9 y^2 == 225 Apply[Subtract]@eq rule = Solve[ F …

After previous calculations, this equation was obtained like this: y == 1 - 2 k + k x How to find the coordinates of the fixed point it passes through? The principle of manual calculation is as follo …

In a triangle, the three inner angles are α, β,γ The trigonometric function relationship equation between the two inner angles is: Cos[α]/(1 + Sin[α]) == Sin[2 β]/(1 + Cos[2 β]) You can obtain this …

Clear["Global`*"] First@Solve[{2 a + 4 d == -16, 9 (a + 4 d) == -36, t == a + (n - 1) d, s == a n + n (n - 1)/2 d}, {t, s}, {a, d}] {t -> 2 (-7 + n), s -> -13 n + n^2}

The known conditions are as follows: Sin[α + β] + Cos[α + β] == 2 Sqrt[2] Cos[α + π/4] Sin[β] Request to find: Tan[α - β] Solve[{Sin[α + β] + Cos[α + β] == 2 Sqrt[2] Cos[α + π/4] Sin[β], tan (α …

Solve[{x^2/a^2 - y^2/b^2 == 1, {x + c, y} . {x - c, y} == 0, a > 0, b > 0, c > 0}, {x, y}] The software keeps prompting for running, but cannot calculate the result. Why?