Question

if x²+1/x²=23 , then find the value of x + 1/x and x³+1 / x³

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Answer 1

$\huge\underline\bold\red{Answer}$

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Given :-

• x²+1/x²=23

To Find:-

• The value of x + 1/x and x³+1 / x³

Solution :-

• ${x}^{2} + \frac{1}{ {x}^{2} } = 23$
• ${x}^{2} + \frac{1}{x ^{2} } + 2 = 25$
• On adding 2 both side.

we have :-

• $(x + \frac{1}{x} ) ^{2} = 25$
• $x + \frac{1}{x} = \sqrt{25}$
• $x + \frac{1}{x} = 5$

value of x + 1/x =$x + \frac{1}{x} = 5$

• [equation 1 ]

To Find the value of x + 1/x and x³+1 / x³

Therefore :-

• $x + \frac{1}{ {x}^{3} } = {5}^{3}$
• ${x}^{3} + \frac{1}{ {x}^{3} } + 3 \times( x + \frac{1}{x} ) = 125$
• [equation 2]

Put the value of [equation 1] in [equation 2]

• ${x}^{3} + \frac{1}{ {x}^{3} } + 3 \times 5 = 125$
• ${x}^{3} + \frac{1}{ {x}^{3} } = 125 - 15$
• ${x}^{3} + \frac{1}{ {x}^{3} } = 110$

Final answer is :-

➖x³+1/x³= 110✔

Answer 2

Step-by-step explanation:

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