Question

7. Calculate x-1/x, when
(a) x² +1/x^2=27 (b)x^4+1/x^4= 727​

Answer 1

Answer:

1.

${x}^{2} + \frac{1}{ {x}^{2} } = 27 \\ = > (x - \frac{1}{x} )^{2} + 2 \times x \times \frac{1}{x} = 27 \\ = > {(x - \frac{1}{x} )}^{2} = 25 \\ = > x - \frac{1}{x} = 5$

2.

${x}^{4} + \frac{1}{ {x}^{4} } = 727 \\ = > {( {x}^{2}) }^{2} + \frac{1}{ ({ {x}^{2}) }^{2} } = 727 \\ = > ({x}^{2} + \frac{1}{ {x}^{2} } )^{2} - 2 = 727 \\ = > ((x - \frac{1}{x} )^{2} + 2) ^{2} = 729 \\ = > {(x - \frac{1}{x} )}^{2} = 27 - 2 \\ = > x - \frac{1}{x} = 5$