Question

If a+b+c=7 and ab+bc+ca=22 find a^2+b^2+c^2

Answer 1

Given:

• a+b+c=7
• ab+bc+ca=22

To find out:

Find a² + b² + c²

Formula used:

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

Solution:

We know that,

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

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

⇒ ( 7 ) ² = a² + b² + c² + 2 × 22

⇒ 49 = a² + b² + c² + 44

⇒ a² + b² + c² = 49 - 44

⇒ a² + b² + c² = 5

Answer 2

$\huge\mathfrak\blue{Answer:}$

Given:

a+b+c=7 and ab + bc + ca=22

To Find:

a^2 + b^2 + c^2

Solution:

We have been given that a+b+c=7 and

ab + bc + ca=22, so inorder to find

a^2 + b^2 + c^2, we can use the formula ( a + b + c )^2.

we know,

( a + b + c )^2 =

a^2 + b^2 + c^2 + 2( ab + bc + ca )

=> (7)^2 = a^2 + b^2 + c^2 + 2(22)

=> 49 = a^2 + b^2 + c^2 + 44

=> 49 - 44 = a^2 + b^2 + c^2

=> 5 = a^2 + b^2 + c^2

OR a^2 + b^2 + c^2 = 5.

Hence, the value of a^2 + b^2 + c^2 is 5.