Question

$\text{Verify that}x\times (x-z)=x\times y-x\times z,if\left(i\right)x=\frac{4}{5},y=-\frac{7}{4}\text{~}andz=3\left(ii\right)x=\frac{3}{4},y=\frac{8}{9}\text{~}andz=-5$

Answer 1

$\left(i\right)x=\frac{4}{5},y=-\frac{7}{4}\text{~}andz=3\text{Using}x\times (y-z)=x\times y-x\times z\Rightarrow \frac{4}{5}\times (\frac{-7}{4}-3)=\frac{4}{5}\times \frac{-7}{4}-\frac{4}{5}\times 3\Rightarrow \frac{4}{5}\times \left(\frac{-7\times 1-3\times 4}{4}\right)=\frac{-7}{5}-\frac{12}{5}\Rightarrow \frac{4}{5}\times \left(\frac{-7-12}{4}\right)=\frac{-7-12}{5}\Rightarrow \frac{4}{5}\times \frac{-19}{4}\Rightarrow \frac{-19}{5}=\frac{-19}{5}\left(ii\right)x=\frac{3}{4},y=\frac{8}{9}\text{~}andz=-5\text{Using}x\times (y-z)=x\times y-x\times z\Rightarrow \frac{3}{4}\times (\frac{8}{9}-(-5\left)\right)=\frac{3}{4}\times \frac{8}{9}-\frac{3}{4}\times (-5)\Rightarrow \frac{3}{4}\times (\frac{8\times 1}{9\times 1}+\frac{5\times 9}{1\times 9})=\frac{2}{3}+\frac{15}{4}\Rightarrow \frac{3}{4}\times \left(\frac{8+45}{9}\right)=\frac{2\times 4}{3\times 4}+\frac{15\times 3}{4\times 3}\Rightarrow \frac{3}{4}\times \frac{53}{9}=\frac{8+45}{12}\Rightarrow \frac{53}{12}=\frac{53}{12}$