Question

are the quadratic equation x^2 - 2x + 1 = 0 the value of x + 1/x is:

Answer 1

QUESTION:

are the quadratic equation x^2 - 2x + 1 = 0 the value of x + 1/x is:

TO FIND:

Value of x.

ANSWER:

GIVEN quadratic equation is in the form of

$a {x}^{2} + bx + c = 0$

we have to factorised it in order to find the zeroes.

1. Split the middle term in such a way that it's sum equal to b i.e -2 and product equal to a ×c which is 1.

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

$(x - 1)(x - 1) \: are \: the \: factors$

now

$x - 1 = 0 \\ x = 1$

$\huge\pink{x = 1}$

so,

we put the value of x in x+1/x ;

$x + \frac{1}{x} \\ 1 + \frac{1}{1} \\ \frac{1 + 1}{1} \\ 2$

$\huge\red{x + \frac{1}{x} = 2}$

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Answer 2

Solution:-

=> x² - 2x + 1 = 0

by mid term splitting.

=> x² - x - x + 1 = 0

=> x ( x - 1 ) - 1 ( x - 1 ) = 0

=> ( x - 1 ) ( x - 1 ) = 0

=> x - 1 = 0 or x - 1 = 0

we get x = 1 from both

=> x = 1

put x = 1 in below

=> x + 1/x

=> 1 + 1/1

=> 1 + 1

=> 2

Hence, x + 1/x = 2

i hope it helps you.