Question

7.Sejam x¹ e x² as raízes da equação x² - 7x +12 = 0. Então a raiz quadrada do número (x¹)² + (x²)² é: a) 10. b) 5. c) 15. d)-25. e) 125.​

Answer 1

$\mathsf{x^2-7x+12=0}$

$\mathsf{\Delta=b^2-4ac}\\\mathsf{\Delta=(-7)^2-4\cdot1\cdot12}\\\mathsf{\Delta=49-48}\\\mathsf{\Delta=1}$

$\mathsf{x=\dfrac{-b\pm\sqrt\Delta}{2a}}\\\\\mathsf{x=\dfrac{-(-7)\pm\sqrt1}{2\cdot1}}\\\\\mathsf{x=\dfrac{7\pm1}{2}}$

$\mathsf{x_{_{1}}=\dfrac{7+1}{2}=\dfrac{8}{2}=4}\\\\\mathsf{x_{_{2}}=\dfrac{7-1}{2}=\dfrac62=3}$

$\mathsf{\sqrt{x_{_{1}}^2+x_{_{2}}^2}=\sqrt{4^2+3^2}=\sqrt{16+9}=\sqrt{25}=\boxed{\boxed{\mathsf{5}}}}$

Resposta: b) 5.

Bons estudos.

Answer 2

Explicação passo-a-passo:

7.Sejam x¹ e x² as raízes da equação x² - 7x +12 = 0. Então a raiz quadrada do número (x¹)² + (x²)² é: a) 10. b) 5. c) 15. d)-25. e) 125.

x²-7x+12=0

a=1; b = -7; c = 12

∆= b²-4ac

∆= (-7)²-4.1.12

∆= 49-48

∆= 1

x = (- b +/- √∆)/2a

x = [-(-7)+/- √1]/2.1

x= (7+/-1)/2

x ' = (7+1)/2= 8/2=4

x" = (7-1)/2= 6/2= 3

4²+3²= 16+9= 25

√25= 5

Resp.: b) 5