Question

question

Answer 1

\(\large \color{black}{\begin{align} & \normalsize \text{If }\ \large a^2+b^2+c^2=1\ \hspace{.33em}\\~\\
& \normalsize \text{then which of the following cannot be a value of }\ \large (ab+bc+ac)\ ? \hspace{.33em}\\~\\
& a.)\ 0 \hspace{.33em}\\~\\
& b.)\ \dfrac12 \hspace{.33em}\\~\\
& c.)\ \dfrac{-1}{4} \hspace{.33em}\\~\\
& d.)\ -1 \hspace{.33em}\\~\\
\end{align}}\)

Answer 2

\[(a + b + c)^2 = 1 + 2 k \Rightarrow 2k + 1 \ge 0 \Rightarrow k \ge -1/2\]

Answer 3

\[(a + b + c)^2 = \underbrace{a^2 + b^2 + c^2}_{\large = ~ 1} + 2 \underbrace{(a b + b c + ca)}_{\large = ~k }\]

Answer 4

Since LHS is \(\ge 0\), RHS is also \(\ge 0\).

Answer 5

why would (a+b+c)^2 be an odd number? 2k+1

Answer 6

it not the odd number he used the formula

\((a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ac)\)