Question

if x square - 3 x + 1 is equal to zero find the value of x square + 1 by x square​

Answer 1

Answer:

7

Step-by-step explanation:

x² - 3x + 1 = 0

x = 3±√9-4/2 = 1/2(3±√5)

x = [3+√5]/ 2 or x = [3 - √5]/2

x² = 1/4[3+√5]² = 1/4[9+5+6√5] = [7+3√5]/2

1/x² = 2/7+3√5 = 2(7-3√5)/49 - 45 = 7-3√5/2

x² + 1/x² = [7+3√5]/2 + [7-3√5]/2

             = 14/2 = 7.

Answer 2

Answer:

The value of $x^2+\frac{1}{x^2}$ is $7$.

Step-by-step explanation:

To find: value of $x^2+\frac{1}{x^2}$.

Consider the quadratic equation as follows:

$x^2-3x+1=0$

Rewrite the equation as follows:

$x^2+1=3x$

Divide the equation by $x$ as follows:

⇒ $\frac{x^2}{x} +\frac{1}{x} =\frac{3x}{x}$

⇒ $x+\frac{1}{x} =3$

Squaring both the sides as follows:

⇒ $(x+\frac{1}{x} )^2=3^2$

Now, simplify as follows:

⇒ $x^2+\frac{1}{x^2}+2x\frac{1}{x} =9$ (Using the formula, $(a+b)^2=a^2+b^2+2ab$)

⇒ $x^2+\frac{1}{x^2}+2 =9$

⇒ $x^2+\frac{1}{x^2} =9-2$

⇒ $x^2+\frac{1}{x^2}=7$

Therefore, $7$ is the required value of $x^2+\frac{1}{x^2}$ when $x^2-3x+1=0$ is given.

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