Question

if a-1/a = 5, find a^2+1/a^2 -3a+3/a

Answer 1

Answer:

$i) \: \: a - \frac{1}{a} = 5 \\ {(a - \frac{1}{a}) }^{2} = {5}^{2} \\ {a}^{2}+ \frac{1}{ {a}^{2} } - 2(a )(\frac{1}{a} ) = 25 \\ {a}^{2} + \frac{1}{ {a}^{2} } - 2 = 25 \\ \boxed{ {a}^{2} + \frac{1}{ {a}^{2} } = 27} ✓\\ ii) \: \: a - \frac{1}{a} = 5 \\ - 3(a - \frac{1}{a} ) =( - 3) \times 5 \\ \boxed{- 3a + \frac{3}{a} = - 15}✓$