if a+b+c=9 and ab+bc+ca=26
find a²+b²+c²
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13
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Given, a+b+c=9 and ab+bc+ca=26.
We know, (a+b+c)
2
=a
2
+b
2
+c
2
+2ab+2bc+2ca
⇒(a+b+c)
2
=a
2
+b
2
+c
2
+2(ab+bc+ca).
Putting the values here, we get,
(9)
2
=a
2
+b
2
+c
2
+2(26)
⇒81=a
2
+b
2
+c
2
+52
⇒a
2
+b
2
+c
2
=81−52=29.
Hence, option D is correct.
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11
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