Question

solve by using quadratic formola x2-3x+1=0​

Answer 1

Answer:

Given Equation:-

• x² - 3x + 1 = 0

To Do:-

• Solve x² - 3x + 1 = 0 using quadratic formula.

Solution:-

Comparing x² - 3x + 1 = 0 with standard quadratic equation i.e. ax² + bx + c = 0, we get

• a = 1

• b = -3

• c = 1

The formula for the discriminant of a quadratic equation is

• D = b² - 4ac

Substituting values for a, b and c

• D = (-3)² - 4(1)(1)

• D = 9 - 4

• D = 5

Now, the formula for finding 'x' using the discriminant is

• x = $\dfrac{-b±\sqrt{D}}{2a}$

Substituting values for b, D and a in the above formula, we get

• x = $\dfrac{3±\sqrt{5}}{2}$

Hence, the values for 'x' are

$\dfrac{3+\sqrt{5}}{2}$ and $\dfrac{3-\sqrt{5}}{2}$

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Answer 2

Answer:

Let the natural number be x² and its square

root be x.

Then, we have

x² + x = 132

x² + x - 132 = 0

x² + 12x - 11x -132 = 0

x (x + 12) - 11 (x +12) = 0

(x+12) (x - 11) = 0

x = -12 and 11

Therefore, the