Given-a-b-3-2c-1-3b-2-c-2-2a-2-a-2-4ac-5c-2-find-b-

Question Number 104811 by bobhans last updated on 24/Jul/20

G i v e n {\begin{cases} a + b \sqrt{3} - 2 c = 1 \\ 3 b^{2} + c^{2} = 2 a^{2} \\ a^{2} + 4 a c = 5 c^{2} \end{cases}

f i n d b

Answered by maths mind last updated on 24/Jul/20

a^{2} + 4 a c = 5 c^{2} \Leftrightarrow (a - c) (a + 5 c) = 0

Answered by bemath last updated on 24/Jul/20

c a s e (1) a = c

\to {\begin{cases} 3 b^{2} = a^{2} \Rightarrow a = \pm b \sqrt{3} \\ b \sqrt{3} = 1 + a = 1 - b \sqrt{3} \end{cases}

2 b \sqrt{3} = 1 \Rightarrow b = \frac{1}{2 \sqrt{3}} = \frac{\sqrt{3}}{6} ★

c a s e (2) a = - 5 c

\to {\begin{cases} 3 b^{2} = 49 c^{2} \Rightarrow c = \pm \frac{b \sqrt{3}}{7} \\ b \sqrt{3} = 1 + 7 c = 1 \pm b \sqrt{3} \end{cases}

2 b \sqrt{3} = 1 \Rightarrow b = \frac{1}{2 \sqrt{3}} = \frac{\sqrt{3}}{6} ★

Facebook Tweet Pin