Basic Maths: Test 41

$\begin{align} & Let\,\,\frac{1}{7}\,\,=a,\frac{1}{2}\,=b\,\,\,and\,\frac{1}{5}\,\,=c \\ & Therefore\,\,\,\,\,\exp ression \\ & =\frac{{{a}^{3}}+{{b}^{3}}+{{c}^{3}}-3abc}{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-ac-bc} \\ & =\frac{\left( a+b+c \right)\left( {{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-ac-bc \right)}{{{a}^{2}}+{{b}^{2}}+{{c}^{2}}-ab-ac-bc}=a+b+c \\ & =\frac{1}{7}+\frac{1}{2}+\frac{1}{5} \\ & =\frac{10+35+14}{70} \\ & =\frac{59}{70} \\ \end{align}$

$\begin{align} & =\frac{{{\left( 3 \right)}^{3}}-{{\left( 0.4 \right)}^{3}}}{{{\left( 3 \right)}^{2}}+3\times 0.4+{{\left( 0.4 \right)}^{2}}} \\ & Let\,\,3\,\,=a,\,0.4\,=b \\ & Therefore\,\,\,\,\exp ression \\ & =\frac{{{a}^{3}}-{{b}^{3}}}{{{a}^{2}}+ab+{{b}^{2}}} \\ & =\frac{\left( a-b \right)\left( {{a}^{2}}+ab+{{b}^{2}} \right)}{{{a}^{2}}+ab+{{b}^{2}}} \\ & =a-b=3-0.4=2.6 \\ \end{align}$

$\begin{align} & =10.9-\left[ 9.8-\left\{ 8.7-\left( 7.6-\overline{6.5-4} \right)\, \right\}\, \right] \\ & =10.9-\left[ 9.8-\left\{ 8.7-\left( 7.6-2.5 \right)\, \right\}\, \right] \\ & =10.9-\left[ 9.8-\left\{ 8.7-4.1\, \right\}\, \right] \\ & =10.9-\left[ 9.8-4.6\, \right] \\ & =10.9-5.2 \\ & =5.7 \\ \end{align}$

$\begin{align} & =\frac{1\frac{1}{10}\div 1\frac{1}{5}}{\left( \frac{11}{12}+1-\frac{5}{6} \right)} \\ & =\frac{\frac{11}{10}\times \frac{5}{6}}{\left( \frac{11+12-10}{12} \right)} \\ & =\frac{\frac{11}{10}\times \frac{5}{6}}{\frac{13}{12}}=\frac{11}{12}\times \frac{12}{13}=\frac{11}{13} \\ \end{align}$

$\begin{align} & 0.9+\sqrt{0.09} \\ & =0.9+0.3=1.2 \\ & 1.4-\frac{1.2}{24} \\ & =1.4-0.05 \\ & =1.35 \\ & 1.5\times 0.89=1.335 \\ & \sqrt{1.21}=1.1 \\ & Hence,\,\,\,the\,\,\,greatest\,\,\,\,number \\ & =1.4-\frac{1.2}{24} \\ \end{align}$