Find the roots of equation : $\displaystyle 81{ y }^{ 2 }-1=0$

The equation 81y squared minus 1 equals 0 can be solved using the algebraic identity for the difference of squares, which states that a squared minus b squared equals the quantity a minus b times the quantity a plus b. Rewriting the equation gives the quantity 9y squared minus 1 squared equals 0, which factors into the quantity 9y minus 1 times the quantity 9y plus 1 equals 0. Setting each factor to zero gives 9y equals 1 and 9y equals negative 1, yielding the roots one ninth and negative one ninth.

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