Question

if a+b=10 and ab = 6 evaluate a³+b³​

Answer 1

Answer:

$a^{3}+ b^{3}=820$

Step-by-step explanation:

$(a+b)^{2} = a^{2} +b ^{2} +2ab\\(10)^{2} = a^{2} +b ^{2} +2(6)\\100-12 = a^{2} +b ^{2} \\.:a^{2} +b ^{2}=88$

We know that,   $a^{3}+ b^{3}=(a+b)( a^{2}+b^{2} -ab)$

$a^{3}+ b^{3}=(a+b)( a^{2}+b^{2} -ab)\\a^{3}+ b^{3}=(10)(88 -6)\\a^{3}+ b^{3}=(10)(82)\\.:a^{3}+ b^{3}=820$

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Answer 2

Answer:

-740

Step-by-step explanation:

a+b=10

ab=6

a*a*a+b*b*b= -740

(a+b)³=a³+b³+3ab(a+b)

(10)³= a³+b³+3×58(10)

1000= a³+b³+1740

1000-1740=a³+b³

a³+b³=-740

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