Question

$if \: x + \frac{1}{x} = 7 \: find \: the \: value \: of \: x ^{2} + \frac{1}{x {}^{2} }$
​

Answer 1

Step-by-step explanation:

given x + 1/x = 7

squaring on both sides

( x + 1/x )² = 7²

x² + 2 (x) (1/x) + (1/x)² = 49

x² + 2 + 1/x² = 49

x² + 1/x² = 49 - 2

x² + 1/x² = 47

Answer 2

Answer:

x=1 or x=6.......

Step-by-step explanation:

$x + \frac{1}{x} = 7 \\ \frac{x ^{2} + 1} {x} = 7 \\ {x}^{2} + 1 = 7x \\ {x}^{2} - 7x + 1 = 0 \\ (x - 1)(x - 6) = 0$

then

x=1 or x=6