Question

Evaluate:

(i) 25³ − 75³ + 50³

(ii) 48³ − 30³ − 18³

(iii) ${\left(\frac{1}{2}\right)}^3+{\left(\frac{1}{3}\right)}^3-{\left(\frac{5}{6}\right)}^3$

(iv) (0.2)³ − (0.3)³ + (0.1)³

Answer 1

In the given problem we have to evaluate the following

(i) Given

We shall use the identity

Let Take

Hence the value of is

(ii) Given

We shall use the identity

Let Take

Hence the value of is

(iii) Given

We shall use the identity

Let Take

Applying least common multiple we get,

Hence the value of is

(iv) Given

We shall use the identity

Let Take

$a^3+b^3+c^3=\left(0.2-0.3+0.1\right)\left(a^2+b^2+c^2-ab-bc-ca\right)+3abc$
$a^3+b^3+c^3=0\times \left(a^2+b^2+c^2-ab-bc-ca\right)+3abc$

Hence the value of is