Question

If a + b= 10,a² +b² =58,find a³ + b³

Answer 1

Answer:

given,a + b = 10, a²+b² = 58

∴ $(a + b) ^{2} = a ^{2} + {b}^{2} + 2ab$

⇒$(10)^{2} = 58 + 2ab$

⇒$100 - 58 = 2ab$

⇒$ab = \frac{42}{2} = 21$

Now,

∴ $a^{3} + {b}^{3} =(a + b)^{3} - 3ab(a + b)$

⇒$(10) ^{3} - 3 \times 21(10)$

⇒$1000 - 630 = 370$

$a^{3} + {b}^{3} = 370$