Question

if x+1/x=2 then find x^2+1/x^2​

Answer 1

Answer:

Step-by-step explanation:

x+1/x=2

As we know that

(a+b)²=a²+b²+2ab

(x+1/x)²=(2)²

x²+1/x²+2=4

x²+1/x²=4-2

x²+1x²=2

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Answer 2

Answer:

$2$

Step-by-step explanation:

$x + \frac{1}{x} = 2 \\ \\ \frac{ {x}^{2} + 1}{x} = 2 \\ \\ {x}^{2} + 1 = 2x \\ \\ {x}^{2} - 2x + 1 \\ \\ {x}^{2} - x - x + 1 \\ \\ x(x - 1) - 1(x - 1) \\ \\ (x - 1)(x - 1) \\ \\ x = 1$

Now,

$The \: Value \: of \: {x}^{2} + \frac{1}{ {x}^{2} } \: is \\ \\ {(1)}^{2} + \frac{1}{ {(1)}^{2} } \\ \\ 1 + 1 \\ \\ 2$