Question

find a square + b square + c square when a + b + c = 5/3
ab + bc + ca = -1/9​

Answer 1

Step-by-step explanation:

As given,

a-b=3=> a=b+3………..(i)

& b-c=5=>c=b-5………….(ii)

Then, c-a=(b-5)-(b+3)=b-5-b-3= -8 .. (iii)

Now, from the question,

a^2 +b^2 +c^2 -ab -bc-ca

Multiplying the above expression by 2 ,we have

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

=2a^2+2b^2+2c^2–2ab-2bc-2ca

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

=(a-b)^2 +(b-c)^2 +(c-a)^2

Putting the values of (a-b),(b-c)&(c-a) from equation (i),(ii)&(iii),we have

=3^2+5^2+(-8)^2

=9+25+64

= 98 Ans.