Question

a + b = 4 ; ab = 3 find 1/a^3 + 1/b^3

Answer 1

$Given \: a + b = 4 \: ---(1) \\and \: ab = 3 \: --(2)$

$i) a^{3} + b^{3} \\= (a+b)^{3} - 3ab(a+b) \\= 4^{3}- 3 \times 4 \times 3 \\= 64 - 36 \\= 28 \: --(3)$

$\red{ Value \: of \:\frac{1}{a^{3}} + \frac{1}{b^{3}} } \\= \frac{b^{3} + a^{3}}{a^{3} b^{3}} \\= \frac{a^{3} + b^{3}}{(ab)^{3}} \\= \frac{ 28}{3^{3}} \\= \frac{28}{27}$

Therefore.,

$\red{ Value \: of \:\frac{1}{a^{3}} + \frac{1}{b^{3}} } \green {= \frac{28}{27}}$

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