Question

if a3+b3:a3-b3=133:117,then a:b:=​

Answer 1

Answer:

$\frac{a}{b} = \frac{5}{2}$

Step-by-step explanation:

$\frac{ {a}^{3} + {b}^{3} }{ {a}^{3} - {b}^{3} } = \frac{133}{117} \\ 117 {a}^{3} + 117{b}^{3} = 133{a}^{3} - 133{b}^{3} \\ 250 {b}^{3} = 16 {a}^{3} \\ \frac{ {a}^{3} }{ {b}^{3} } = \frac{250}{16} \\ \frac{ {a}^{3} }{ {b}^{3} } = \frac{125}{8} \\ \frac{a}{b} = \frac{5}{2}$

Answer 2

a:b is 5:2

Step-by-step explanation:

Given that,

$\dfrac{a^3+b^3}{a^3-b^3}=\dfrac{133}{117}$

On cross multiplying, we get :

$117a^3+117b^3=133a^3-133b^3$

On rearranging a on LHS and b on RHS,

$117a^3-133a^3=-133b^3-117b^3\\\\-16a^3=-250b^3\\\\16a^3=250b^3\\\\\dfrac{a^3}{b^3}=\dfrac{250}{16}\\\\\dfrac{a^3}{b^3}=\dfrac{125}{8}$

Taking cube roots on both sides we get :

$\dfrac{a}{b}=\dfrac{5}{2}$

So, it is clear that a:b is 5:2. Hence, this is the required solution.

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