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If (a+b+c)=16 and a^2+b^2+c^2=80 find value of ab+bc+ca |
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Answer» • a + b + c = 16 • a² + b² + c² = 80TO Find :• AB + bc + ca Solution : Using the identity : Put the values : Value of ab + bc + ca = 88 Few USEFUL Identities : • (a+b)² = a² + 2ab + b²• (a-b)² = a² - 2ab + b²• (a+b)(a-b) = a² - b²• (a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca• (a+b)³ = a³ + b³ +3AB(a+b)• (a-b)³ = a³ - b³ - 3ab(a-b)• a³ + b³ = (a+b)(a² - ab + b²)• a³ - b³ = (a-b)(a² + ab + b²)• a³ + b³ + c³ -3abc = (a+b+c)(a² + b² + c² - ab - bc - ca)• a³ + b³ + c³ -3abc = ½(a+b+c) {(a-b)² + (b-c)² + (c-a)² }• If a + b + c = 0,then a³ + b³ + c³ = 3abc |
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