Question

If a² + b² + 2a + 1 = 0, then find value of $\frac{2a + b}{3}$

Answer 1

Question:-

If a² + b² + 2a + 1 = 0, then find value of $\sf\frac{2a + b}{3}.$

Given:-

• a² + b² + 2a + 1 = 0.

To Find:-

Value of $\sf\frac{2a + b}{3}.$

Solution:-

a² + b² + 2a + 1 = 0.

ax² + bx + c = 0.

Comparing with,

• a = 1.
• b = 2.
• c = b² + 1.

$\sf \large x = \frac{ - b± \sqrt{b {}^{2} - 4ac } }{2a} \\ \\ \sf \large a = \frac{ - 2± \sqrt{4 - 4(b {}^{2} + 1) } }{2} \\ \\ \sf \large a = - 1± \sqrt{1 - b {}^{2} - 1 } \\ \\ \sf \large a = - 1±bi$

Comparing with real and imaginary parts.

• a = – 1.
• b = 0.

$\sf \large \frac{2a + b}{ 3 } = \frac{2 \times ( - 1) + 0}{3} = - \frac{ 2}{3}$

Answer:-

$\sf \large \green{ \therefore The \: value \: of \:of \: \frac{2a + b}{3} = - \frac{2}{3} . }$

Hope you have satisfied. ⚘