Question

Find the value of 8a^3 + 27b^3 if 2a + 3b = 21/2 and ab= 5/6.

Answer 1

Answer:

8a³+27b³ = 8001/8

Explanation:

It is given that,

2a+3b = 21/2 ----(1)

ab = 5/6 --------(2)

Now ,

8a³+27b³

= (2a)³+(3b)³

= (2a+3b)³ -3×2a×3b(2a+3b)

= (21/2)³ - 18ab×(21/2)

= (21/2)³ - 18×(5/6)(21/2)

= (21/4)[(441/2)- 30]

= (21/4) [ (441-60)/2]

= (21/4)(381/2)

= 8001/8

••••

Answer 2

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

$\bf\huge{\implies 2a + 3b=\dfrac{21}{2}}$        

$\bf\huge{\implies ab=\dfrac{5}{6}}$  

Find value of 8a³ + 27b³

Factorise the number

= (2a)³ + (3b)³

= (2a + 3b)³ - 3 × 2a × 3b(2a + 3b)

$\bf\huge{\implies(\dfrac{21}{2})^3 - 18ab\times \dfrac{21}{2}}$  

Substitute the value of ab

$\bf\huge{\implies(\dfrac{21}{2})^3 - 18\times\dfrac{5}{6}\times \dfrac{21}{2}}$

$\bf\huge{\implies\dfrac{21}{4} \times \dfrac{441}{2}-30}$        

$\bf\huge{\implies\dfrac{21}{4}\times \dfrac{441-60}{2}}$        

$\bf\huge{\implies\dfrac{21}{4}\times\dfrac{381}{2}}$        

$\bf\huge\bf\huge{\boxed{\bigstar{{\dfrac{8001}{8}}}}}$