Question

If a+b+c = 12, and ab+bc+ca = 22, then find the value of a^2+b^2+c^2

Answer 1

GIVEN :

a+b+c=12

ab+bc+ca=22

a^2+b^2+c^2=?

We know that

(a+b+c)^2=a^2+b^2+c^2+2(ab+bc+ba)

(12)^2=a^2+b^2+c^2+2(22)

144=a^2+b^2+c^2+44

144-44=a^2+b^2+c^2

100=a^2+b^2+c^2

Answer 2

Step-by-step explanation

▪️A/Q, the given values are

▪️a+b+c = 12

▪️a^2 + b^2 + c^2 = 64

▪️Now, the value we need to find is ab + bc + ca. This can be determined by using the expansion of (a + b + c)^2

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

▪️2 (ab+bc+ca) = (a+b+c)^2 - (a^2+b^2+c^2)

▪️(ab+bc+ca) = [(a+b+c)^2 - (a^2+b^2+c^2)]/2

▪️= [(12^2) - (64)]/2

▪️= (144 - 64)/2

▪️= 80/2

▪️ab + bc + ca = 40

▪️Therefore,

▪️ab + bc + ca = 40

Hopes it help you❤️❤️