Question

determine o valor de X nos casos

Answer 1

Boa noite!

1)
${b}^{2} = {a}^{2} + {c}^{2} - 2 \times a \times c \times \cos(60) \\ {x}^{2} = {16}^{2} + {10}^{2} - 2 \times 16 \times 10 \times \frac{ 1}{2} \\ {x}^{2} = 256 + 100 - 320 \times \frac{ 1}{2} \\ {x}^{2} = 256 + 100 - 160 \\ {x}^{2} = 196 \\ x = \sqrt{196} = 14$
Resposta : 14

2)

${14}^{2} = {x}^{2} + {6}^{2} - 2 \times x \times 6 \times \cos(120) \\ 196 = {x}^{2} + 36 -12x \times \frac{ - 1}{2} \\ { - x}^{2} = 36 - 196 + 6x \\ { - x}^{2} = - 160 + 6x \\ { - x}^{2} - 6x + 160 = 0 \\ delta = {b}^{2} - 4 \times a \times c \\ delta = 36 - 4 \times ( - 1) \times 160 \\ delta = 36 + 640 \\ delta = 676 = \sqrt{676} = 26 \\ \\ x1 = \frac{6 + 26}{ - 2} = - 16 \: falso \\ \\ x2 = \frac{6 - 26}{ - 2} = \frac{ - 20}{ - 2} = 10 \: verdade$
Resposta: 10.

Espero ter ajudado!