Question

If a+b+c=11 and ab+bc+ca=36 find the value of a2+b2+c2

Answer 1

Answer: a²+b²+c²=49

Step-by-step explanation:

(a+b+c)² = a²+b²+c²+2ab+2bc+2ca

(11)² = a²+b²+c²+2(ab +bc +ca)

121= a²+b²+c² +2(36)

121-72 =a²+b²+c²

49=a²+b²+c²

Answer 2

Given,

$a + b + c = 11$

$ab + bc + ca = 36$

To Find,

$a^{2} + b^{2} + c^{2} = ?$

Solution,

We can solve the question using the following ways:

From the formula,

$(a + b + c)^{2} = a^{2} + b^{2} + c^{2} + 2(ab + bc + ca)$

Substituting the given values,

$(11)^{2} = a^{2} + b^{2} + c^{2} + 2(36)$

$121 = a^{2} + b^{2} + c^{2} + 72$

$49 = a^{2} + b^{2} + c^{2}$

Hence, the value of $a^{2} + b^{2} + c^{2}$ is equal to 49.