Question

if x + 1 by x is equal to 4

a) show that x square + 1 by x square = 14
b) x to the power 4 + 1 by x to the power 4 = 194.​

Answer 1

Step-by-step explanation:

(a)

$x + \frac{1}{x} = 4 \\ or,(x + \frac{1}{x } )^{2} = {4}^{2} \\or, {x}^{2} + 2 \times x \times \frac{1}{x} + \frac{1}{ {x}^{2} } = 16 \\ or, {x}^{2} + 2 + \frac{1}{ {x}^{2} } = 16 \\ or, {x}^{2} + \frac{1}{ {x}^{2} } = 16 - 2 \\ or, {x}^{2} + \frac{1}{ {x}^{2} } = 14 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: (hence \: showed )$

(b)

$x + \frac{1}{x} = 4 \\or,(x + \frac{1}{x} )^{2} = {4}^{2} \\ or, {x}^{2} + 2 \times x \times \frac{1}{x} + \frac{1}{ {x}^{2} } = 16 \\ or, {x}^{2} + 2 + \frac{1}{ {x}^{2} } = 16 \\ or, {x}^{2} + \frac{1}{ {x}^{2} } = 16 - 2 \\ or, {x}^{2} + \frac{1}{ {x}^{2} } = 14 \\ or, {( {x}^{2} + \frac{1}{ {x}^{2} }) }^{2} = {14}^{2} \\ or, {( {x}^{2}) }^{2} + 2 \times {x}^{2} \times \frac{1}{ {x}^{2} } + { (\frac{1}{ {x}^{2} }) }^{2} = 196 \\ or, {x}^{4} + 2 + \frac{1}{ {x}^{4} } = 196 \\ or, {x}^{4} + \frac{1}{ {x}^{4} } = 196 - 2 \\ or, {x}^{4} + \frac{1}{ {x}^{4} } = 194 \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: (hence \: showed)$

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