Question

If x + 1/x =5, find value of x^4 +1/x^4

Answer 1

Answer:

257

Step-by-step explanation:

x+1=5x

1/4=X

(1/4)^4+1/(1/4)^4

1/256+1/1/256

257/256×256

257

Answer 2

Given :-

• x + 1/x = 5

To find :-

• x⁴ + 1/x⁴

Solution :-

• Here, we are given x + 1/x = 5

Identity used :-

• (a + b)² = a² + b² + 2ab

$\qquad\small\underline{\pmb{\sf \:Squaring \: both\: sides:-}}$

$\pink{\qquad\leadsto\quad \pmb {\mathfrak{ (x +\dfrac{1}{x } )² = (5)²  }}}$

$\qquad\leadsto\quad \pmb {\mathfrak{ x² + \dfrac{1}{x²} + 2 \times x \times \dfrac{1}{x }= 25  }}$

$\qquad\leadsto\quad \pmb {\mathfrak{ x² + \dfrac{1}{x²} + 2 = 25  }}$

$\qquad\leadsto\quad \pmb {\mathfrak{ x² + \dfrac{1}{x²}= 25 - 2  }}$

$\qquad\leadsto\quad \pmb {\mathfrak{ x² +\dfrac{1}{x²} = 23  }}$

$\qquad\leadsto\quad \pmb {\mathfrak{ \big(x² + \dfrac{1}{x²}\big )² = (23)²  }}$

$\qquad\leadsto\quad \pmb {\mathfrak{ (x²)² + (\dfrac{1}{x})² + 2 \times x² \times \dfrac{1}{x²} = 529  }}$

$\qquad\leadsto\quad \pmb {\mathfrak{ x⁴ + \dfrac{ 1}{x⁴ } + 2 = 529  }}$

$\qquad\leadsto\quad \pmb {\mathfrak{ x⁴ +\dfrac{ 1}{x⁴ } = 529 - 2  }}$

$\pink{\qquad\leadsto\quad \pmb {\mathfrak{ x⁴ +\dfrac{ 1}{x⁴ }= 527  }}}$

• The value of x⁴ + 1/x⁴ is 527

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