Question 63

The value of (0.7 × 0.7 × 0.7 - 0.6 × 0.6 × 0.6) ÷ (0.7 × 0.7 + 0.6 × 0.6 + 0.7 × 0.6) is:

Solution

Expression : (0.7 × 0.7 × 0.7 - 0.6 × 0.6 × 0.6) ÷ (0.7 × 0.7 + 0.6 × 0.6 + 0.7 × 0.6)

Substituting 0.7 with a and 0.6 with b, we get :

= $$\frac{a^3 - b^3}{a^2 + b^2 + ab}$$

Using, $$(x^3 - y^3) = (x - y) (x^2 + y^2 + xy)$$

= $$\frac{(a - b) (a^2 + b^2 + ab)}{(a^2 + b^2 + ab)}$$

= $$a - b = 0.7 - 0.6$$

= $$0.1$$

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