Trivial 1

Algebra Level 3

1 a + 1 b ≠ 1 a + b \dfrac{1}{a} + \dfrac{1}{b} \neq \dfrac{1}{a+b}

True or False: The above statement holds for any real numbers a , b a,b satisfying a , b , a + b ≠ 0 a,b,a+b \neq 0 .

True False

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1 solution

Rishabh Jain
Jan 14, 2016

For equality to hold, ( a + b ) 2 = a b (a,b,a+b ≠ 0. ) (a+b)^2=ab\space\space \text{(a,b,a+b} \neq 0.) Rearranging and substituting a b = t \frac{a}{b}=t ,we get t 2 + t + 1 = 0 t^2+t+1=0 which has imaginary roots. Therefore equality cannot hold for real numbers.

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why the answer is "true"??????

Chaitnya Shrivastava - 5 years, 4 months ago

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The statement given is about the inequality, which always holds... hence true...

Rishabh Jain - 5 years, 4 months ago

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oh ! sorry I did not notice it and got it wrong.

Chaitnya Shrivastava - 5 years, 4 months ago

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