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a+b = a/b +b/a, then find the value of a 2 +b 2 . The answer is 2 but can someone please prove it how?? please help quick

a+b = a/b +b/a, then find the value of a2 +b2 . The answer is 2 but can someone please prove it how?? please help quick

Grade:12

1 Answers

Mahesh Madhavan
21 Points
6 years ago
Given, a+b=(\frac{a}{b})+(\frac{b}{a}).
\Rightarrow (a+b)*ab = a^2 + b^2
\Rightarrow (a^2b + ab^2) = a^2 + b^2
\Rightarrow a^2 - a^2b + b^2 - ab^2 = 0
\Rightarrow a^2(1-b) + b^2(1-a)=0
In the above equation, because a and b are real, the equation will be valid only if:-
(1-a)= (1-b)= 0,
because a^2  and  b^2  are always positive for real numbers a and b
 
So,a=b=1 
 
Thus, a^2 + b^2 =2

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