If we multiply both sides by 2 we get 2xy = x+y. Subtract y from both sides and get 2xy - y = x. Factor out y on the left and get y(2x-1) = x. Divide both sides by 2x-1 and get y = x/(2x-1). Let

The only integer solutions are a=1,b=1 and a=0, b=0. Here is why ab=1/2 (a+b) 2ab=a+b 2ab-b = a b(2a-1) = a b = a/(2a-1) This shows that there are infinitely many solutions if we

Hi Prashant, Yes. When the power is expressible as a fraction p/r, then x^(p/r) equals the rth root of x^p. When the power is a non-repeating decimal and cannot be expressed as a fraction, we can

It is known that ln(2.3^4.2) = 4.2*ln(2.3). From this, do the exponential on both sides. This gives e^ln(2.3^4.2) = e^[4.2*ln(2.3)]. Since the exponential and ln() are inverses, the lest side reduces

Hi Prashant, Simple harmonic motion involves an ordinary differential equation rather than a partial differential equation. For it to be a partial differential equation, the derivative(s) must be those

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