Question

of a +b = 10 and a² + b ² = 59, find value of
a^3 +b^3​

Answer 1

Answer:

$a³+b²=385$

Step-by-step explanation:

Given that:

$a+b=10$

$a²+b²=59$

Then,

$(a+b)²=a²+b²+2ab$

$→10²=59+2ab$

$→2ab=100-59=41$

$→ab=20.5$

Then,

$(a+b)³=a³+b³+3ab(a+b)$

$→10³=a³+b³+3×20.5×10$

$→1000=a³+b³+30×20.5$

$→1000=a³+b³+615$

$→1000-615=a³+b³$

$→a³+b³=1000-615$

$→\boxed{a³+b³=385}$

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Answer 2

Answer:

a³+b³=385

Step-by-step explanation:

given a² + b ²=59

a+b=10

squaring

(a+b)²=100

a² + b ²+2ab=100

59+2ab=100

2ab=41

ab=41/2

Now a³+b³=(a+b)(a² + b ²-ab)

=10*(59-41/2)

=10*(118-41)/2

=5*77=385