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If a+b+c=9 and a b+b c+c a=23 , then a^2...

If `a+b+c=9` and `a b+b c+c a=23` , then `a^2+b^2+c^2=?` (a)35 (b) 58 (c) 127 (d) none of these

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`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`
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