Question

A+b+c=9and ab+bc+ca=23 find a²+b²+c²

Answer 1

a³+b³+c³- 3abc = (a+b+c) (a²+b²+c²-ab-bc-ca)

a+b+c= 9 (given)

ab+ bc + ca = 23 (given)

⇒ a³+b³+c³- 3abc = 9 (a²+b²+c²- 23)            ... (1)

 (a+b+c)²= a²+b²+c²+ 2ab+ 2bc+ 2ca

92= a²+b²+c²+ 2(ab+bc+ca)

81= a²+b²+c²+ 2(23)

81 = a²+b²+c²+ 46

a²+b²+c²= 81-46
a²+b²+c² = 35

Answer 2

Answer:

a²+b²+c²=35

Step-by-step explanation:

Formula used,

(a+b+c)²=a²+b²+c²+2ab+2bc+2ca

also, it can be written as,

a²+b²+c²+2(ab+bc+ca)

Now,as given in the question,

a+b+c=9 and ab+bc+ca=23

implies,

(9)²=a²+b²+c²+2(23)

implies,

81-46=a²+b²+c²

therefore,

a²+b²+c²=35

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