Practicing Success
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If \( {x }^{ 2} \) + x = 19 find \( {(x + 5) }^{ 2} \) + \(\frac{1}{(x+5)^2}\) |
77 79 81 83 |
79 |
Let x + 5 = t x = t - 5 Put in \( {x }^{ 2} \) + x = 19 ⇒ (t - 5)2 + t - 5 = 19 ⇒ t2 + 25 - 10t + t - 5 = 19 ⇒ t2 - 9t + 1 = 0 ⇒ t + \(\frac{1}{t}\) = 9 ⇒ t2 +\(\frac{1}{ {t }^{2 }}\) = 92 - 2 = 79 |
