+1206 If \(x+y=\frac{7}{12}\) and \(x-y=\frac{1}{12}\), what is the value of \(x^2-y^2\)? Express your answer as a common fraction.
+36916 Add the two equations together to get
2x = 8/12
x = 4/12
from the first equation then 4/12 + y = 7/12 means y = 3/12
then (4/12)^2 - (3/12)^2 = (1/3)^2 - (1/4)^2 = 1/9 - 1/16 = 16/144 - 9/144 = 7/144
+26367 If
\(x+y=\dfrac{7}{12} \)
and
\(x-y=\dfrac{1}{12}\),
what is the value of \(x^2-y^2\)?
Express your answer as a common fraction.
\(\begin{array}{|rcll|} \hline (x-y)(x+y) &=& \dfrac{7}{12}\times \dfrac{1}{12} \quad | \quad (x-y)(x+y) = x^2-y^2 \\ \mathbf{x^2-y^2} &=& \dfrac{7}{12}\times \dfrac{1}{12} \\ &=&\mathbf{ \dfrac{7}{144}} \\ \hline \end{array} \)
