Super Rational!

Number Theory Level 2

Is there any rational number satisfying the following?

R × I R \times I = R ′ R' , where R and R' are Rational number and I is Irrational number.

No, it is impossible Yes, it is possible

Vaibhav Priyadarshi by Vaibhav Priyadarshi , 17, India

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1 solution

Zero, the Only Rational which when multiplied by any number equals Zero.

Zero multiplied by any Irrational is again zero which is rational.

So, The rational * irrational = rational' is possible.

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0 × I = 0 ⟹ I = 0 0 0\times I = 0 \implies I = \dfrac{0}{0} is undefined. So 0 0 is not the solution.

Naren Bhandari - 3 years, 2 months ago

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You can't transpose 0 on right side. After 1st step, your one step is hidden that is dividing both sides by 0. Then on LHS, you got (0*I)/0.

On the LHS, you got I, this is because you have cancelled 0 by 0 which is invalid!

Vaibhav Priyadarshi - 3 years, 2 months ago

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