Question

if a+b=9 and ab=20 find a3 +b3​

Answer 1

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$a+b=9\:\:\:\:\: and \:\:\:\:\;ab=20$

now......

$a {}^{2} + b {}^{2} = (a + b) {}^{2} - 2ab \\ = > a {}^{2} + b {}^{2} = 9 {}^{2} - 2(20) \\ = > a {}^{2} + b {}^{2} = 41$

therefore......

$a {}^{3} + b {}^{3} = (a + b)(a {}^{2} + b {}^{2} - ab) \\ = > a {}^{3} + b {}^{3} = (9)(41 - 20) \\ = > a {}^{3} + b {}^{3} =18 9$

$\large\mathcal{hope\: this \: helps \:you......}$

Answer 2

SOLUTION:

Given,

• a+b=9
• ab=20

Find,

• a³+b³=?

So,

(a+b)³ = a³+b³+3ab(a+b)

(9)³ = a³+b³+3×20(9)

729 = a³+b³+60(9)

729 = a³+b³+540

a³+b³ = 729-540

a³+b³ = 189.