Question

a)
x²-5x+4<0.

b)
²-5x+4>0.

c)
x-6r+9>0.

(quero os cálculos)

se não souber não responde (´ . .̫ . `)

boa tarde ♥️
​

Answer 1

$\Large\boxed{\begin{array}{l}\tt a)~\sf x^2-5x+4<0\\\underline{\rm fac_{\!\!,}a}\\\sf f(x)=x^2-5x+4\\\underline{\rm Ra\acute izes~de~f(x):}\\\sf x^2-5x+4=0\\\sf\Delta=b^2-4ac\\\sf\Delta=(-5)^2-4\cdot1\cdot4\\\sf\Delta=25-16\\\sf\Delta=9\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\sf x=\dfrac{-(-5)\pm\sqrt{9}}{2\cdot1}\\\\\sf x=\dfrac{5\pm3}{2}\begin{cases}\sf x_1=\dfrac{5+3}{2}=\dfrac{8}{2}=4\\\\\sf x_2=\dfrac{5-3}{2}=\dfrac{2}{2}=1\end{cases}\\\sf f(x)>0~se~x<1~ou~x>4\\\sf f(x)<0~se~1<x<4\end{array}}$

$\Large\boxed{\begin{array}{l}\sf Desejamos~saber~para~quais~valores~de~x\\\sf teremos~f(x)<0~portanto~a~resposta~\\\sf da~inequac_{\!\!,}\tilde ao~dada~\acute e\\\sf S=\{x\in\mathbb{R}/1<x<4\}\\\sf para~concluir~isto~veja~anexo~1.\end{array}}$

$\Large\boxed{\begin{array}{l}\tt b)~\sf x^2-5x+4<0\\\underline{\rm fac_{\!\!,}a}\\\sf f(x)=x^2-5x+4\\\underline{\rm Ra\acute izes~de~f(x):}\\\sf x^2-5x+4=0\\\sf\Delta=b^2-4ac\\\sf\Delta=(-5)^2-4\cdot1\cdot4\\\sf\Delta=25-16\\\sf\Delta=9\\\sf x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\sf x=\dfrac{-(-5)\pm\sqrt{9}}{2\cdot1}\\\\\sf x=\dfrac{5\pm3}{2}\begin{cases}\sf x_1=\dfrac{5+3}{2}=\dfrac{8}{2}=4\\\\\sf x_2=\dfrac{5-3}{2}=\dfrac{2}{2}=1\end{cases}\\\sf f(x)>0~se~x<1~ou~x>4\\\sf f(x)<0~se~1<x<4\end{array}}$

$\Large\boxed{\begin{array}{l}\sf Desejamos~saber~para~quais~valores~de~x\\\sf teremos~f(x)>0~portanto~a~resposta\\\sf da~inequac_{\!\!,}\tilde ao~dada~\acute e\\\sf S=\{x\in\mathbb{R}/x<1~ou~x>4\}\\\sf Para~concluir~isto~veja~anexo~2.\end{array}}$

$\Large\boxed{\begin{array}{l}\tt c)~\sf x^2-6x+9>0\\\underline{\rm Fac_{\!\!,}a}\\\sf g(x)=x^2-6x+9\\\sf fatorando~a~express\tilde ao~teremos\\\sf g(x)=(x-3)^2\\\underline{\rm Ra\acute izes~de~g(x):}\\\sf (x-3)^2=0\\\sf x-3=0\\\sf x=3\\\sf a~par\acute abola~tangenciar\acute a~o~eixo~x~no~ponto~3.\\\sf portanto~teremos~valores~positivos~para~todo~x\ne3.\\\sf portanto\\\sf S=\{x\in\mathbb{R}/x\ne3\}\\\sf para~concluir~isto~veja~anexo~3.\end{array}}$