Question

Find the value of mn +no+om, ifm+n+o=12 and m2 +n2+o2=64.​

Answer 1

Answer:

(mn + no + om) = 40

Step-by-step explanation:

Given that-

m + n + o = 12

$m^{2}+n^{2}+o^{2} = 64$

mn + no + om =?

We know that-

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

So, $(m+n+o)^{2} = m^{2}+n^{2}+o^{2}+2(mn+no+om)$

But, m + n + o = 12 and

$m{2}+n^{2}+o^{2} = 64$

So, $(12)^{2} = 64+2(mn+no+om)$

$144 = 64 +2(mn+no+om)$

144 - 64 = 2(mn + no + om)

80 = 2(mn + no + om)

$(mn+no+om) = \dfrac{80}{2}$

So, (mn + no + om) = 40