a, b, c are three real numbers such that
a + b + c = 7, a^2
+ b^2
+ c
^2
= 35 and
a
^3
+ b^3
+ c
^3
= 151. Find the value of abc.
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a+b+c = 7
(a+b+c)² = a²+b²+c²+2(ab+bc+ca)
ab+bc+ca = ((a+b+c)² - (a²+b²+c²))/2 = (7²-35)/2 = 7
(a+b+c)³ = a³+b³+c³+3(ab+bc+ca)(a+b+c)-3abc
abc = ((a+b+c)³ - a³+b³+c³-3(ab+bc+ca)(a+b+c))/3 = (343-151-3*7*7)/3 = 15
(a+b+c)² = a²+b²+c²+2(ab+bc+ca)
ab+bc+ca = ((a+b+c)² - (a²+b²+c²))/2 = (7²-35)/2 = 7
(a+b+c)³ = a³+b³+c³+3(ab+bc+ca)(a+b+c)-3abc
abc = ((a+b+c)³ - a³+b³+c³-3(ab+bc+ca)(a+b+c))/3 = (343-151-3*7*7)/3 = 15
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