Question

1 If a + b + c = 9 and ab + bc + ca = 23, then find :
a² + b 2 + c²​

Answer 1

Given:

• (a + b + c) = 9
• (ab + bc + ca) = 23

To find:

a² + b² + c² = ?

Solution:

For solving such questions, we use the below formula:

☞ (a + b + c)² = a² + b² + c² + 2(ab + bc + ac)

Substitute the given values in the above formula

➥ (9)² = a² + b² + c² + 2(23)

➝ 81 = a² + b² + c² + 46

➝ 81 - 46 = a² + b² + c²

➝ a² + b² + c² = 35

∴ a² + b² + c² = 35

KNOW MORE:

$\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textbf{\textsf{Algebraic\:Identity}}\:\bigstar}\\\\1)\bf\:(a+b)^{2} = a^{2} + 2ab + b^{2}\\\\2)\sf\: (a-b)^{2} = a^{2} - 2ab + b^{2}\\\\3)\bf\: a^{2} - b^{2} = (a+b)(a-b)\\\\4)\sf\: (a+b)^{2} = (a-b)^{2} + 4ab\\\\5)\bf\: (a-b)^{2} = (a+b)^{2} - 4ab\\\\6)\sf\: (a+b)^{3} = a^{3} + 3ab(a+b) + b^{3}\\\\7)\bf\:(a-b)^{3} = A^{3} - 3ab(a-b) + b^{3}\\\\8)\sf\: a^{3} + b^{3} = (a+b)(a^{2} - ab + b^{2})\\\\\end{minipage}}$