Question

If x-1/x=5,find the value of (x^2+1/x^2) and (x^4+1/x^4)​

Answer 1

GIVEN:-

• If $\rm{x - \dfrac{1}{x} = 5}$.

TO FIND :-

• The Value of $\rm{x^2 + \dfrac{1}{x^2}}$ & $\rm{x^4 + \dfrac{1}{x^4}}$.

Now,

$\implies\rm{x - \dfrac{1}{x} = 5}$.

$\implies\rm{(x - \dfrac{1}{x})^2 = (5)^2 }$

$\implies\rm{ 25 = x^2 + \dfrac{1}{x^2} -2\times{x}\times{\dfrac{1}{x}}}$

$\implies\rm{ 25 + 2 = x^2 + \dfrac{1}{x^2}}$

$\implies\rm{ 27 = x^2 + \dfrac{1}{x^2}}$.

Now again,

$\implies\rm{ x^2 + \dfrac{1}{x^2}= 27}$.

$\implies\rm{ (x^2 + \dfrac{1}{x^2})^2= (27)^2}$

$\implies\rm{ (x^2)^2 + \dfrac{1}{(x^2)^2} - 2\times{x^2}\times{\dfrac{1}{x^2}}}$

$\implies\rm{ 729 = x^4 + \dfrac{1}{x^4} +2}$

$\implies\rm{ 729 - 2 =x^4 + \dfrac{1}{x^4}}$

$\implies\rm{ 727 = x^4 + \dfrac{1}{x^4}}$.

Answer 2

Answer:

⭐ Question ⭐

If x-1/x=5, find the value of (x²+1/x²) and (x⁴+1/x⁴)

⭐ Given :-

✏ If x-1/x = 5

⭐ To find :-

✏ The value of x²+1/x² and x⁴+1/x⁴

⚫ Now,

=> x-1/x = 5 ( Squaring both sides we get)

=> (x-1/x)² = (5)²

=> x²+1/x²-2×x×1/x = 25

=> x²+1/x² 25+2

=> x²+1/x² = 27

✔ The value of x²+1/x² is 27

⚫ Now again,

=> x²+1/x² = 27 ( Squaring both sides we get)

=> (x²+1/x²)² = (27)²

=> (x²)²+1/(x²)²-2×x²×1/x² = 729

=> x⁴+1/x⁴+2 = 729

=> x⁴+1/x⁴ = 729-2

=> x⁴+1/x⁴ = 727

✔ The value of x⁴+1/x⁴ is 727

Step-by-step explanation:

HOPE IT HELP YOU