Question

if a³+b³ = -54, a+b = 4, then ab=?​

Answer 1

★GIVEN:-

$\implies \orange{a³+b³ = -54, a+b = 4}$

★find:-

$\implies \red{ab=?}$

solution

$\implies \orange{a³+b³ = -54} - - (1)$

$\implies \: a + b = 4 - - - (2)$

do square both sides

$\implies \: (a + b) {}^{2} = 4 {}^{2} \\ \\ \\ \implies \: a {}^{2} + b {}^{2} + 2ab = 16 \\ \\ \\ \implies a {}^{2} + b {}^{2} = 16 - 2ab - - - (3)$

EQ (1) solve

$\implies \: a {}^{3} + b {}^{3} = - 54 \\ \\ \\ \implies \: (a + b)(a {}^{2} + b {}^{2} - ab) = - 54$

• put value EQ (2) and eq(3) value

$\implies \: ( 4)(16 - 2ab - ab) = - 54 \\ \\ \\ \\ \implies \: 16 - 3ab = \frac{ - 54}{4} \\ \\ \\ \implies \: - 3ab = \frac{ - 27}{2} - 16 \\ \\ \\ \implies \: - 3ab = \frac{ - 27 - 32}{2} \\ \\ \\ \implies \: - ab = \frac{ - 59}{3 \times 2} \\ \\ \\ \implies \: ab = \frac{59}{6} \\ \\ \\ \implies \: ab = 9.634$

answer

$\implies \star \pink{ab = 9.634}$

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I hope it helps you