x^2-4x+3>0 eching | Microsoft math hal qiluvchi

x uchun yechish

Grafik

Viktorina

Quadratic Equation

5xshash muammolar:

Veb-qidiruvdagi o'xshash muammolar

https://math.stackexchange.com/questions/907079/directly-prove-that-2x2-4x-3-0-for-all-real-x

https://socratic.org/questions/we-have-p-x-an-polynomial-that-meets-the-conditions-rest-of-dividing-p-x-with-x-

https://socratic.org/questions/how-to-use-the-discriminant-to-find-out-how-many-real-number-roots-an-equation-h-5

Baham ko'rish

Klipbordga nusxa olish

x^{2}-4x+3=0

Tengsizlikni yechish uchun chap tomon faktorini hisoblang. Kvadrat koʻp tenglama bu orqali hisoblanadi: ax^{2}+bx+c=a\left(x-x_{1}\right)\left(x-x_{2}\right), bu yerda x_{1} va x_{2} ax^{2}+bx+c=0 kvadrat tenglamaning yechimlari.

x=\frac{-\left(-4\right)±\sqrt{\left(-4\right)^{2}-4\times 1\times 3}}{2}

ax^{2}+bx+c=0 shaklidagi barcha tenglamalarni bu formula bilan yechish mumkin: \frac{-b±\sqrt{b^{2}-4ac}}{2a}. Kvadrat tenglamada a uchun 1 ni, b uchun -4 ni va c uchun 3 ni ayiring.

x=\frac{4±2}{2}

Hisoblarni amalga oshiring.

x=3 x=1

x=\frac{4±2}{2} tenglamasini ± plus va ± minus boʻlgan holatida ishlang.

\left(x-3\right)\left(x-1\right)>0

Yechimlardan foydalanib tengsizlikni qaytadan yozing.

x-3<0 x-1<0

Koʻpaytma musbat boʻlishi uchun x-3 va x-1 ikkalasi yo manfiy, yo musbat boʻlishi kerak. x-3 va x-1 ikkalasi manfiy boʻlganda, yechimini toping.

x<1

Ikkala tengsizlikning mos yechimi – x<1.

x-1>0 x-3>0

x-3 va x-1 ikkalasi musbat boʻlganda, yechimini toping.