Question

a+b=11,ab=28 find the value of a3+1/a3

Answer 1

Solve and get the answer

Answer 2

$Given \:a + b = 11 \: ---(1) \: and \\ab = 28\: ---(2)$

$i ) ( a - b )^{2} = ( a + b )^{2} - 4ab \\= 11^{2} - 4 \times 28 \\= 121 - 112 \\= 9 \\= 3^{2}$

$a - b = 3 \: ---(2)$

/* Adding equations (1) and (2) , we get *\

$\implies 2a = 14$

$\implies a = \frac{14}{7}$

$\implies a = 7 \: ---(3)$

$Now, Value \: of \: a^{3} + \frac{1}{a^{3}} \\= 7^{3} + \frac{1}{7^{3}}\\= 343 + \frac{1}{343} \\= \frac{ 117649+1}{343} \\= \frac{117650}{343}$

Therefore.,

$\red {Value \: of \: a^{3} + \frac{1}{a^{3}}} \\\green{ = \frac{117650}{343} }$

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