Question

Evaluate: $\frac{(7.5{)}^2+(8.5{)}^2-2\times 7.5\times 8.5}{{10}^2-6^2}$

• A.
  
  $\frac{1}{64}$
  
• B.
  
  $\frac{11}{5}$
  
• C.
  
  $\frac{1}{23}$
  
• D.
  
  $\frac{3}{19}$
  

Answer 1

The correct option is A


$\frac{1}{64}$

$\frac{(7.5{)}^2+(8.5{)}^2-2\times 7.5\times 8.5}{{10}^2-6^2}$
* $a^2-b^2=(a+b)(a-b)$
* $x^2+y^2-2xy=(x-y{)}^2$
$=\frac{(7.5-8.5{)}^2}{(10+6)(10-6)}=\frac{(-1{)}^2}{16\times 4}=\frac{1}{64}$
So, the correct answer is option (a).