Question

If a+b =10 and ab=21, find the value of a cube +b cube

Answer 1

$\colorbox{black}{ \color{white}{solution}}$


Given that : -

(a + b) = 10 and ab = 21.
$a {}^{3} + b {}^{3} = ? \:$

Now,

(a + b) = 10

=> (a + b)² = (10)² [squaring both sides .]

=> a² + b² + 2ab = 100

=> a² + b² = 100 - (2 × 21)

=> a² + b² = 100 - 42

=> a² + b² = 58

Now,
---------

a³ + b³

= (a + b)(a² - ab + b²)

Putting the values ,we get,

= 10 × [(a² + b²) - ab]

= 10 × (58 - 21)

= 10 × 37

= 370

$\colorbox{yellow}{so} \: \boxed{a { }^{3} + b {}^{3} = 370}$