Question

20. Solve by using quadratic formula : x2-3x+1=0.

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Answer 1

Hey there here is your AnsweR,

Appropriate Question :

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

Required Solution :

Solving by using Quadric formula :

$✰\:\: \tt \: x ^ { 2 } -3x+1=0$

All equations of the form $ax^{2}+bx+c=0$ can be solved using the quadratic formula: $\frac{-b±\sqrt{b^{2}-4ac}}{2a}.$ The quadratic formula gives two solutions, one when ± is addition and one when it is subtraction.

$: \implies \tt \: x^{2}-3x+1=0$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute 1 for a, -3 for b, and 1 for c in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}.$

$: \implies \tt \: x=\frac{-\left(-3\right)±\sqrt{\left(-3\right)^{2}-4}}{2}$

Square -3.

$: \implies \tt \: x=\frac{-\left(-3\right)±\sqrt{9-4}}{2}$

The opposite of -3 is 3.

$: \implies \tt \: x=\frac{3±\sqrt{5}}{2}$

Now solve the equation $x=\frac{3±\sqrt{5}}{2}$ when ± is plus. Add 3 to $\sqrt{5}.$

$: \implies \tt \: x=\frac{\sqrt{5}+3}{2}$

Now solve the equation $x=\frac{3±\sqrt{5}}{2}$ when ± is minus. Subtract $\sqrt{5}$from 3.

$: \implies \tt \: x=\frac{3-\sqrt{5}}{2}$

The equation is now solved.

$✰ \: \: \underline{ \boxed{ \frak{x=\frac{\sqrt{5}+3}{2}}}} \: \: ✰\\ ✰ \: \:\underline{ \boxed{ \frak{x=\frac{3-\sqrt{5}}{2} }}} \: \: ✰$

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