Question

Find the value of a3 - b3, if a-b = 5/7 and ab = 7/3. ,

Answer 1

Answer:

1840/343

Explanation:

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We know the algebraic identity:

a³-3a²b+3ab²-b³ = (a-b)³

Or

a³ - b³ = (a-b)³ +3ab(a-b)

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Here ,

a-b = 5/7 ----( 1 )

ab = 7/3 ------( 2 )

Now ,

a³ - b³ = (a-b)³ + 3ab(a-b)

= (5/7)³ + 3×(7/3)(5/7)

=125/343 + 5/1

= (125+1715)/343

= 1840/343

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Answer 2

$\bf\huge\textbf{\underline{\underline{According\:to\:the\:Question}}}$  

Using Identity ⇒ a³ - b³ = (a - b)³ + 3ab (a-b)

${\implies a - b = \dfrac{5}{7}}$        

${\implies ab = \dfrac{7}{3}}$

Put value in the Identity we get

${\implies(\dfrac{5}{7})^3 + 3\times\dfrac{7}{3}\times \dfrac{5}{7}}$        

${\implies\dfrac{125}{343} + \dfrac{5}{1}}$

${\implies\dfrac{125 + 1715}{343}}$

${\implies\dfrac{1840}{343}}$