Question

find the value of a^2+b^2+c^2 if a+b+c=13 and ab+bc+ca=27​

Answer 1

❥ Given : a + b + c = 13 $\textsf{and}$ ab + bc + ca = 27

❥ To Find : Value of a² + b² + c²

$\rule{315}{3}$

$\longrightarrow$ a + b + c = 13

• Squaring on Both Sides of the Equation

$\longrightarrow$ (a + b + c)² = 13²

$\longrightarrow$ a² + b² + c² + 2ab + 2bc + 2ca = 169

• Taking 2 as common

$\longrightarrow$ a² + b² + c² + 2(ab + bc + ca) = 169

• Substitute the Given Values

$\longrightarrow$ a² + b² + c² + 2(27) = 169

$\longrightarrow$ a² + b² + c² + 54 = 169

• Subtract 54 from Both Sides

$\longrightarrow$ a² + b² + c² + 54 - 54 = 169 - 54

$\longrightarrow$ a² + b² + c² = 115