Find ab+bc+ca if a+b+c=9 and a square +b square+c sqare=35
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a+b+c=9
⇒(a+b+c)²=81 (squaring both sides)
⇒a²+b²+c²+2(ab+bc+ca)=81 (using the identity)
⇒35 + 2(ab+bc+ca)=81 (putting the value of a²+b²+c²)
⇒2(ab+bc+ca)=46
(ab+bc+ca)=23
ans. the value of ab+bc+ca is 23
⇒(a+b+c)²=81 (squaring both sides)
⇒a²+b²+c²+2(ab+bc+ca)=81 (using the identity)
⇒35 + 2(ab+bc+ca)=81 (putting the value of a²+b²+c²)
⇒2(ab+bc+ca)=46
(ab+bc+ca)=23
ans. the value of ab+bc+ca is 23
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