Ratsional tenglamalar
Javoblar ota-onalar va o‘qituvchilar uchun.
1
4/(x − 3) = 5/(x + 1) ni yeching.
4(x + 1) = 5(x − 3) ⇒ x = 19; maxrajlar nolga teng emas. Javob: 19.
2
(x² − 3x − 10)/(x − 5) = 0 ni yeching.
x² − 3x − 10 = (x − 5)(x + 2); ildizlar 5, −2; x = 5 chet ildiz. Javob: x = −2.
3
1/x + 1/(x + 1) = 3/2 ni yeching.
2(x + 1) + 2x = 3x(x + 1) ⇒ 3x² − x − 2 = 0, D = 25, x = 1 yoki x = −2/3; ikkalasi ham maxrajni nolga aylantirmaydi.
4
(x/(x − 1))² − 5 · x/(x − 1) + 6 = 0 ni almashtirish bilan yeching.
t = x/(x − 1): t² − 5t + 6 = 0, t = 2 yoki 3. t = 2 ⇒ x = 2; t = 3 ⇒ x = 3/2. Javob: 2; 3/2.
5
Sistemani yeching: 1/x + 1/y = 5/6, xy = 6.
(x + y)/(xy) = 5/6 ⇒ x + y = 5; xy = 6 ⇒ (2; 3) va (3; 2).