solvefor x,(λ^2-9)x^2+(λ^2-16)y^2=λ

解

解く

x, (λ^{2} - 9) x^{2} + (λ^{2} - 16) y^{2} = λ

x = \frac{λ - y ^{2} ( λ ^{2} - 16 )}{λ ^{2} - 9}, x = - \frac{λ - y ^{2} ( λ ^{2} - 16 )}{λ ^{2} - 9}; λ \neq = 3, λ \neq = - 3

解答ステップ

(λ^{2} - 9) x^{2} + (λ^{2} - 16) y^{2} = λ

(λ^{2} - 16) y^{2}

を右側に移動します

(λ^{2} - 9) x^{2} = λ - (λ^{2} - 16) y^{2}

以下で両辺を割る

λ^{2} - 9; λ \neq = 3, λ \neq = - 3

x^{2} = \frac{λ - y ^{2} ( λ ^{2} - 16 )}{λ ^{2} - 9}; λ \neq = 3, λ \neq = - 3

x^{2} = f (a)

の場合, 解は

x = f (a), - f (a)

x = \frac{λ - y ^{2} ( λ ^{2} - 16 )}{λ ^{2} - 9}, x = - \frac{λ - y ^{2} ( λ ^{2} - 16 )}{λ ^{2} - 9}; λ \neq = 3, λ \neq = - 3