Question

Solve:
${\left(6\frac{4}{11}\right)}^2-{\left(4\frac{7}{11}\right)}^2$

Answer 1

${\left(6\frac{4}{11}\right)}^2-{\left(4\frac{7}{11}\right)}^2$

$={\left(\frac{70}{11}\right)}^2-{\left(\frac{51}{11}\right)}^2$

$=\frac{{\left(70\right)}^2-{\left(51\right)}^2}{{\left(11\right)}^2}$

$=\frac{(70+51)(70-51)}{{\left(11\right)}^2}$ $(a^2-b^2=(a+b)(a-b))$

$=\frac{121(70-51)}{121}$ $({\left(11\right)}^2=121)$

$=19$

Hence, the answer is $19.$