y+(x^4-+x5)/((x+3)^(1/2)) −6 −5 −4 −3 −2 −1 0 1 2 3 4 5 6 −3 -2.5 −2 -1.5 −1 -0.5 0 0.5 1 1.5 2 2.5 3 x y
Exercícioy = x ( x 3 − 5 ) x + 3 y=\frac{x\left(x^3-5\right)}{\sqrt{x+3}} y = x + 3 x ( x 3 − 5 )
Solução explicada passo a passo
1
Aplicamos a regra: a 3 + b a^3+b a 3 + b = ( a − ∣ b ∣ 3 ) ( a 2 + a ∣ b ∣ 3 + ∣ b ∣ 2 3 ) =\left(a-\sqrt[3]{\left|b\right|}\right)\left(a^2+a\sqrt[3]{\left|b\right|}+\sqrt[3]{\left|b\right|^{2}}\right) = ( a − 3 ∣ b ∣ ) ( a 2 + a 3 ∣ b ∣ + 3 ∣ b ∣ 2 ) a = x a=x a = x b = − 5 b=-5 b = − 5
y = x ( x − 5 3 ) ( x 2 + 5 3 x + ( 5 ) 2 3 ) x + 3 y=\frac{x\left(x-\sqrt[3]{5}\right)\left(x^2+\sqrt[3]{5}x+\sqrt[3]{\left(5\right)^{2}}\right)}{\sqrt{x+3}} y = x + 3 x ( x − 3 5 ) ( x 2 + 3 5 x + 3 ( 5 ) 2 )
Resposta final para o problema y = x ( x − 5 3 ) ( x 2 + 5 3 x + ( 5 ) 2 3 ) x + 3 y=\frac{x\left(x-\sqrt[3]{5}\right)\left(x^2+\sqrt[3]{5}x+\sqrt[3]{\left(5\right)^{2}}\right)}{\sqrt{x+3}} y = x + 3 x ( x − 3 5 ) ( x 2 + 3 5 x + 3 ( 5 ) 2 )