Question

$ifa + b = 8and \: ab = 6find \: the \: value \: of \: a {}^{3} + b {}^{3}$
please solve it​

Answer 1

Step-by-step explanation:

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Answer 2

Given,

• a + b = 8
• ab = 6

To Find,

• a³ + b³ = ?

Solution :

We Know that :

$\boxed{\sf{\pink{(a + b)^{3} = a^{3} + b^{3} + 3ab(a + b)}}}$

Here, Value Put

• a + b = 8
• ab = 6

$\implies \sf{(8)^{3} =a^{3} + b^{3} + 3 \times 6 \times 8 }$

$\implies \sf{512 = a^{3} + b^{3} + 144}$

$\implies \sf{a^{3} + b^{3} = 512 - 144}$

$\implies \boxed{\sf{a^{3} + b^{3} = 368}}$

$\rule{200}2$

$\underline{\boxed{\bold{\pink{Other \ Identities:}}}}$

$\implies \sf{a^{2} + b^{2} = (a + b) - 2ab}$

$\implies \sf{a^{2} + b^{2} = (a-b) + 2ab}$

$\implies \sf{(a + b)^{3} = a^{3} + b^{3} + 3ab(a + b)}$

$\implies \sf{a^{3} + b^{3} = (a + b) (a^{2} + b^{2} - ab)}$

$\implies \sf{ a^{3} + b^{3} + c^{3} -3abc = (a+b+c)(a^{2} + b^{2}+ c^{2}- ab - bc - ca)}$