Question

if a+b=10,a^2 +b^2 =58,find the value of a^3+b^3

Answer 1

@
(a+b)=10
a²+b²= 58
We know that
(a+b)²=a²+b²+2ab
(10)²=58+2ab
100=58+2ab
100-58= 2ab
42= 2ab
21= ab
Now ,
(a+b)³=a³+b³+3ab(a+b)
(10)³=a³+b³+3*21(10)
1000=a³+b³+63(10)
1000=a³+b³+630
1000-630=a³+b³
370=a³+b³
@:-)

Answer 2

we know that,

(a+b)^2=a^2+b^2+2ab

(10)^2= 58+2ab

100=58+2ab

100-58=2ab

42=2ab

21=ab

Now,

(a+b)^3=a^3+b^3+3ab(a+b)

(10)^3=a^3+b^3+3*21(10)

1000=a^3+b^3+63(10)

1000=a^3+b^3+630

1000-630=a^3+b^3

370= a^3+b^3

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