Question

If a+b+c=10 and ab+bc+ca=20. Find the value of a² +b² + c²​

Answer 1

Step-by-step explanation:

(a+b+c)²=a²+b²+c²+2ab+2bc+2ca

a²+b²+c²= (a+b+c)²-2ab-2bc-2ca

a²+b²+c²= (10)²-2(ab+bc+ca)

a² +b² + c²= (10)²-2(20)

a²+b²+c²= 100-40

a²+b²+c²= 60

Answer 2

EXPLANATION.

• GIVEN

a + b + c = 10

ab + bc + ca = 20

$\large \bold \green{ \underline{to \: \: find \: \: value \: \: of \: \: {a}^{2} + {b}^{2} + {c}^{2} }}$

Formula of ( a + b + c)^2

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

$(10) {}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(20)$

$100 = {a}^{2} + {b}^{2} + {c}^{2} + 40$

$100 - 40 = {a}^{2} + {b}^{2} + {c}^{2}$

$60 = {a}^{2} + {b}^{2} + {c}^{2}$

Therefore,

value of a^2 + b^2 + c^2 = 60