Question

If a+b+c= 7 and ab + bc + ca = 20, find the value of of
${a}^{2} + {b}^{2} + {c}^{2}$
​

Answer 1

Answer:

a²+b²+c²=9

Step-by-step explanation:

Given:-

a+b+c=7 & ab+bc+ca=20

To Find:-

a²+b²+c²

Formula Used:-

(a+b+c)²=a²+b²+c²+2(ab+bc+ca)

Solution:-

(a+b+c)²=a²+b²+c²+2(ab+bc+ca)

(7)²=a²+b²+c²+2(20)

49=a²+b²+c²+40

a²+b²+c²=49-40

a²+b²+c²=9

Answer 2

Step-by-step explanation:

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

${7}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 40 \\ so \: {a}^{2} + {b}^{2} + {c}^{2} = 40 - 49 = - 9$

${a}^{2} + {b}^{2} + {c}^{2}$= -9