the value of A2+b2+c2, if a +b+c=13 and ab+bc+ca=27
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215 is the value of a²+b²+c², if a +b+c=13 and ab+bc+ca=27
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Given
a + b + c = 13
ab + bc + ca = 27
To find
The value of a² + b² + c²
The identities with use in this question
(a + b + c)² = a² + b² + c² + 2(ab + bc + ac)
Where
a + b + c = 13 ,ab + bc + ca = 27
We get
(13)² = a² + b² + c² + 2(27)
169 = a² + b² + c² + 54
a² + b² + c² = 169 - 54
a² + b² + c² = 115
Answer
a² + b² + c² = 115
More identities
(a + b)² = a² + b² + 2ab
(a - b)² = a² + b² - 2ab
(a + b)(a - b) = a² - b²
(a + b + c)² = a² + b² + c² + 2(ab + bc + ac)
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