Question

if a+b+c=8 and ab + bc+ ca=17, then find the value of a²+ b²+ c²​

Answer 1

Hope this is helpful

Please Mark it as Brainlist answer

Answer 2

${\huge{\boxed{\boxed{\mathcal{\pink{QUESTION\ddot{\smile}}}}}}}$

If a+b+c = 8 and ab+bc+ca = 17 , then find the value of a²+b²+c² .

${\huge{\boxed{\boxed{\red{\mathcal{ANSWER\checkmark}}}}}}$

★ Concept :

• In these type of Questions , we just use the formulas to solve .

• You must remember the formulas , which we have to use in the question .

• ( a + b + c )² = a² + b² + c² + 2( ab + bc + ca )

★ We have :

• a + b + c = 8
• ab + bc + ca = 17

★ To Find :

• a² + b² + c² = ?

★ Solution :

$\rm \: {a} + b + c = 8$

$\tt \: squaring \: both \: sides.$

$\mapsto \rm \: {(a + b + c)}^{2} = {8}^{2}$

$\mapsto \rm \: {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) = 64$

Since ,

We have the value of (ab + bc + ca) so ,

Put its value in this equation .

$\mapsto \rm {a}^{2} + {b}^{2} + {c}^{2} + 2 \times 17 = 64$

$\mapsto \rm \: {a}^{2} + {b}^{2} + {c}^{2} + 34 = 64$

$\mapsto \rm \: {a}^{2} + {b }^{2} + {c}^{2} = 64 - 34$

$\mapsto \boxed{ \rm \: {a}^{2} + {b}^{2} + {c}^{2} = 30}$

So , the answer would be 30 .

★ Some Important Formulas :

• (a+b)² = a² + b² + 2ab
• (a-b)² = a² + b² - 2ab
• (a+b+c)² = a² + b² + c² + 2(ab + bc + ca)
• (a+b-c)² = a² + b² + c² + 2( ab - bc - ac )
• (a-b-c)² = a² + b² + c² + 2(-ab + bc - ac)
• (a-b+c)² = a² + b² + c² + 2(-ab-bc+ac)
• (-a-b-c)² = (a+b+c)²