How do you solve this equation: x²-4x+4=0?
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With the pq formula
Hardcore
Diese Gleichung ist eine quadratische Gleichung, also können wir sie lösen, indem wir die quadratische Formel verwenden:
𝑥=−𝑏±𝑏2−4𝑎𝑐2𝑎
x=2a
−b±b2
−4ac
Für die Gleichung 𝑥2−4𝑥+4=0
x2
−4x+4=0 haben wir:
𝑎=1,𝑏=−4,𝑐=4
a=1,b=−4,c=4
Einsetzen in die quadratische Formel:
𝑥=−(−4)±(−4)2−4(1)(4)2(1)
x=2(1)
−(−4)±(−4)2
−4(1)(4)
𝑥=4±16−162
x=2
4±16−16
𝑥=4±02
x=2
4±0
Da die Quadratwurzel von 0 gleich 0 ist, haben wir:
𝑥=4±02
x=2
4±0
Das bedeutet, dass beide Lösungen übereinstimmen:
𝑥=42=2
x=2
4
=2
Also ist die einzige Lösung für die Gleichung 𝑥2−4𝑥+4=0
x2
−4x+4=0 𝑥=2
x=2.
Note:
The second binary formula (a-b)2 =a2 -2ab+b2 can be used on the left side of the equation. For a=x and b=2, then nämlch (x−2)2=x2−4x+4 is obtained.
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Possible solution path:
This is a square equation:
x^2 + b x + c = 0
to dissolve according to the formula
x = (-b +- sqrt(b^2 – 4ac)/(2a)
Here is a=1, b=−4, c=4, so that:
x = (4 +- sqrt(4^2 – 4*4))/2
x=2
With the midnight formula.
{-b ± √(b2 – 4ac)} ÷ 2a
In your example, a= 1; b= -4; c= 4
If you need a more detailed answer or explanation then write me privately
pq formula
Result is 1+ root from 8 and 1 root from 8
Best with the PQ formula