Question

If a+b=6,ab=11/4 find the value of 2a^3-2b^3​

Answer 1

8(a-b) ( a² + ab + b² ) is your answer

Answer 2

$Given \: a + b = 6 \: --(1)$

$ab = \frac{11}{4} \: --(2)$

$i) (a-b)^{2} = (a+b)^{2} - 4ab$

$= 6^{2} - 4 \times \frac{11}{4}$

$= 36 - 11$

$= 25$

$a - b= \sqrt{25} = 5 \: --(3)$

$\red{ The \: value \: of \: 2a^{3} - 2b^{3} }$

$= 2(a^{3} - b^{3} )$

$= 2[ (a-b)^{3} + 3ab(a-b)]$

$= 2[ 5^{3} + 3\times \frac{11}{4} \times 5 ]$

$= 2[ 125 + \frac{165}{4} ]$

$= 2 [ \frac{500 + 165 }{4} ]$

$= \frac{665}{2}$

$= 332.5$

Therefore.,

$\red{ The \: value \: of \: 2a^{3} - 2b^{3} }$

$\green { = 332.5}$

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