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Algebra> a+b = a/b +b/a, then find the value of a ...

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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

Shashwat , 8 Years ago

Grade 12

1 Answers

Mahesh Madhavan

$Given, a+b=(\frac{a}{b})+(\frac{b}{a})$ .

$\Rightarrow (a+b)*ab = a^2 + b^2$

$\Rightarrow (a^2b + ab^2) = a^2 + b^2$

$\Rightarrow a^2 - a^2b + b^2 - ab^2 = 0$

$\Rightarrow a^2(1-b) + b^2(1-a)=0$

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, $a^2 + b^2 =2$

Last Activity: 8 Years ago

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