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2017-03-23 Algebra - Solution:

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

2017-03-23 Algebra - Solution to an equation:

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

2017-03-22 Geometry - Decimal Number Indices:

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

2017-03-22 Algebra - Decimal Number Indices.:

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

2017-03-12 Geometry - Simple Harmonic Motion:

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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