Question

The value of \[\frac{(0 . 013 )^3 + (0 . 007 )^3}{(0 . 013 )^2 - 0 . 013 \times 0 . 007 + (0 . 007 )^2}\] is

Options

• 0.006

• 0.02

•  0.0091

•  0.00185

Answer 1

The given expression is

 \[\frac{(0 . 013 )^3 + (0 . 007 )^3}{(0 . 013 )^2 - 0 . 013 \times 0 . 007 + (0 . 007 )^2}\]

Assume a = 0.013and b = 0.007. Then the given expression can be rewritten as

`(a^+b^3)/(a^2 - ab + b^2)`

Recall the formula for sum of two cubes

`a^3 +b^3 = (a+b )(a^2 - ab + b^2)`

Using the above formula, the expression becomes

`((a+b)(a^2 - ab + b^2))/(a^2 - ab + b^2)`

Note that both  a and b are positive. So, neither `a^3 +b^3`nor any factor of it can be zero.

Therefore we can cancel the term `(a^2 - ab+b^2)`from both numerator and denominator. Then the expression becomes

`((a+b)(a^2 - ab + b^2))/(a^2 - ab + b^2) = a+b`

                                         ` = 0.013 + 0 .007`

                                        ` = 0.02`