Question 56

If $$a : b = b : c$$, then what is the value of $$a^{6} : b^{6}$$?

Solution

$$a : b = b : c$$

$$\frac{a}{b}\ =\ \frac{b}{c}$$

$$ac=b^2$$

$$b^2 = ac$$ Eq.(i)

Value of $$a^{6} : b^{6}$$ = $$a^{6} : (ac)^{3}$$ [Put Eq.(i) here.]

= $$a^{6} : a^{3}c^{3}$$

= $$a^{3} : c^{3}$$

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