QQuestion
If \frac{(a+b)^3}{(a-b)^3}=\frac{64}{27}:
(a) Find \frac{a+b}{a-b}.
(b) Hence, using properties of proportion, find a : b.
✓Answer
(a) Given:
\frac{(a+b)^3}{(a-b)^3}=\frac{64}{27} \left(\frac{a+b}{a-b}\right)^3=\frac{4^3}{3^3}Taking the cube root of both sides:
\frac{a+b}{a-b}=\frac{4}{3}(b) Using the above proportion:
3(a + b) = 4(a − b)
⇒ 3a + 3b = 4a − 4b
⇒ 4a − 3a = 3b + 4b
⇒ a = 7b
⇒ a/b = 7/1
Therefore, a : b = 7 : 1.
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