Question

If
$x - \frac{1}{x} = 5$
Then find :-
(I)
${x}^{2} + \frac{1}{ {x}^{2} }$
(II)
${x}^{4} + \frac{1}{ {x}^{4} }$
(Tell the answer only if you know because I don't want it to be wrong)

(Give me the full solution not only the answer)

(Best answer will be marked as Brainliest)

(Answer all questions)

(Stupid Answers will be reported)

Answer 1

(x-1/x)^2=x^2+1/x^2 -2x×1/x
5^2=x^2+1/x^2 -2
25+2=x^2+1/x^2
x^2+1/x^2=27
is your answer

Answer 2

Hey !!!

x - 1/x = 5

•°• ( a - b ) ² = a² + b - 2ab

similarly

(x - 1/x )² = x² + 1/x² - 2x×1/x

5² = x² + 1/x² -2

25 + 2 = x² + 1/x²

x² + 1/x² = 27 -----1) 1st Answer ✔

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now , 1/x⁴ + 1/x⁴

(1/x²)² + (1/x²)² can i write ?

hence, similarly

hence, a² + b² = ( a + b) ² - 2ab

since,

x⁴ + 1/x⁴ = ( x² + 1/x² ) ² - 2x² ×1/x²

x⁴ + 1/x⁴ = 27² - 2

x⁴ + 1/x⁴ = 729 - 2 ----[from 1st equation ]


x⁴ + 1/x⁴ = 727Answer

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Hope it helps you !!!

@Rajukumar111