Solve the Simple Equation: 1/d^2 = 1/(81m^2) + 1/(25m^2) in Just a Few Steps!

[superwolf]

How can I solve this equation:

<br /> \frac{1}{d^2} = \frac{1}{(9m)^2} + \frac{1}{(5m)^2}<br />

?

Try:

<br /> \frac{1}{d^2} = \frac{1}{81m^2} + \frac{1}{25m^2} \Rightarrow d^2 = 81m^2 + 25m^2 = 106m^2 \Rightarrow d = 10.3m<br />

 

[HallsofIvy]

How can I solve this equation:

<br /> \frac{1}{d^2} = \frac{1}{(9m)^2} + \frac{1}{(5m)^2}<br />

?

Try:

<br /> \frac{1}{d^2} = \frac{1}{81m^2} + \frac{1}{25m^2}

up to here you are fine. But

\Rightarrow d^2 = 81m^2 + 25m^2 = 106m^2 \Rightarrow d = 10.3m<br />

is not true. if
\frac{1}{a}= \frac{1}{b}+ \frac{1}{c}
it is NOT true that a= b+ c.
More specifically,
\frac{1}{\frac{1}{b}+ \frac{1}{c}}\ne b+ c

I recommend that you multiply both sides of the equation by the least common divisor of all three fractions, (25)(81)d².

 

[Mark44]

Or even better, by (25)(81)d²m²