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If x2 + x = 5, find the value of \({\left( {x + 3} \right)^3} + \frac{1}{{{{\left( {x\; + \;3} \right)}^3}}}\)
If x2 + x = 5, find the value of \({\left( {x + 3} \right)^3} + \frac{1}{{{{\left( {x\; + \;3} \right)}^3}}}\)
1). 110
2). 112
3). 114
4). 116
1 answers
1 vote
Let (x + 3) = m
x + 3 = m
x = m - 3
Put the value of ‘x’
x2 + x = 5
(m - 3)2 + (m - 3) = 5
m2 + 9 - 6m + m - 3 = 5
m2 - 5m + 1 = 0
m2 + 1 = 5m
$({\rm{m}} + \frac{1}{{\rm{m}}} = 5)$
Now
$({{\rm{m}}^3} + \frac{1}{{{{\rm{m}}^3}}} = {5^3} - 3 \times 5)$
$({{\rm{m}}^3} + \frac{1}{{{{\rm{m}}^3}}} = 110)$
Put the value of m = x + 3
Then,
$({\left( {{\rm{x}} + 3} \right)^3} + \frac{1}{{{{\left( {x + 3} \right)}^3}}} = 110)$