Question

cho \(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=2\);\(\frac{1}{a^2}+\frac{1}{b^2}+\frac{1}{c^2}=2\)

cmr        a+b+c=abc

Answer 1

(1/a+1/b+1/c)=2

=>(1/a+1/b+1/c)²=2²=4

=>1/a²+1/b²+1/c²+2(1/ab+1/bc+1/ca)=4

=>2(1/ab+1/bc+1/ca)=4-(1/a²+1/b²+1/c²)=4-2=2 

=>1/ab+/bc+1/ca=1

=>(a+b+c)/abc=1

=>a+b+c=abc

Answer 2

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