Question

if a+b=10,ab=21 find the valu of a^3+b^3

Answer 1

the value of identity
$( {x}^{3} + {y}^{3} ) = (x + y)( {x}^{2} - xy + {y}^{2} )$
now put the value of a+b=10,ab=21
$= (10)( ( {x + y})^{2} + 2xy - xy) \\ = 10( {10}^{2} + xy) \\ = 10(100 + 21)$
$= 10 \times 121 \\ = 1210$

Answer 2

a³+b³=(a+b)(a²-ab+b²)

we should find a²+b²
 (a+b)²=a²+2ab+b²
 (10)²= a²+b²+2×21
100 = a²+b²+42
100-42=58=a²+b²

a³+b³=(a+b)(a²+b²-ab)
        =10(58-21)
        =10×37=370