Algebra · qiyin

Algebraik kasrlar bo‘yicha savol

$\dfrac{\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{2}{ab}-\dfrac{c^2}{a^2b^2}}{\left(\dfrac{c}{ab}-\dfrac{1}{a}-\dfrac{1}{b}\right)(a+b+c)}$ ifodaning qiymatini $a=2{,}4;\ b=\dfrac{5}{6}$ va $c\ne\pm(a+b)$ bo‘lganda hisoblang.

A. $-\dfrac{1}{2}$
B. $-2$
C. $\dfrac{1}{2}$
D. $-\dfrac{1}{4}$

Javob va yechimni ko‘rish

Javob: $-\dfrac{1}{2}$

Surat $\dfrac{(a+b-c)(a+b+c)}{a^2b^2}$, maxraj $-\dfrac{(a+b-c)(a+b+c)}{ab}$. Nisbat $-1/(ab)$ va $ab=2$, demak javob $-1/2$.

Mavzuni mustahkamlang

Bu savol Algebraik kasrlar mavzusiga tegishli. Ta’riflar, formulalar va misollarni mavzu sahifasida ko‘ring.

Mavzuni o‘rganish

Shu mavzudagi boshqa savollar

Ifodani soddalashtiring: $\frac{x^2 - 9}{x^2 + 6x + 9} \cdot \frac{x + 3}{x - 3}$Kasrlarni ayiring: $\frac{2a}{a^2 - b^2} - \frac{1}{a - b}$Tenglamani yeching: $\frac{x}{x-2} - \frac{2}{x-2} = 1$Ifodani soddalashtiring: $\left(\frac{1}{x} + \frac{1}{y}\right) : \frac{x^2 - y^2}{xy}$Agar $x + \frac{1}{x} = 5$ bo'lsa, $x^2 + \frac{1}{x^2}$ ning qiymatini toping.