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Sodda irratsional tenglamalar

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10.08.2023

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SODDA IRRATSIONAL TENGLAMALAR O‘zgaruvchisi ildiz ostida qatnashgan tenglama irratsional tenglamalar deyiladi.√ ???????????? ?????? − ???????????? = ???????????? √ ?????? ?????? − ?????? ?????? + ?????? = ?????? + ?????? √ ?????? ?????? + ?????? ?????? − ?????? = √ − ?????? ?????? − ?????? ( ?????? ?????? + ?????? ?????? + ?????? ) √ ?????? + ?????? = ?????? SODDA IRRATSIONAL TENGLAMALAR √ ?????? ( ?????? ) = ?????? ( ?????? ) ⟺ { ?????? ( ?????? ) ≥ ?????? ?????? ( ?????? ) = ?????? ?????? ( ?????? ) √ ?????? ( ?????? ) = ?????? , ?????? < ?????? ⟹ ?????? ∈ ∅ √ ?????? ( ?????? ) = ?????? , ?????? ≥ ?????? ⟹ ?????? ( ?????? ) = ?????? ?????? ?????? ?????? √ ?????? ( ?????? ) = ?????? ( ?????? ) ⟺ { ?????? ( ?????? ) ≥ ?????? ?????? ( ?????? ) = ?????? ?????? ?????? ( ?????? )IRRATSIONAL TENGLAMALAR Javob: tenglamani yeching.?????? = ?????? ?????????????????????????????????????????? : √ ?????? ( ?????? ) = ?????? ( ?????? ) ⟺ { ?????? ( ?????? ) ≥ ?????? ?????? ( ?????? )= ?????? ?????? ( ?????? ) { ?????? − ?????? ≥ ?????? ?????? + ?????? ?????? − ?????? ?????? = ?????? ?????? − ?????? ?????? + ?????? { ?????? ≥ ?????? ?????? ?????? ?????? − ?????? ?????? = ?????? { ?????? ≥ ?????? [ ?????? = ?????? ?????? = ?????? MISOLLAR YECHISH ?????????????????????????????????????????? : ?????? ( ?????? ) √ ?????? ( ?????? ) = ?????? ⟺ [ ?????? (?????? )= ?????? { ?????? ( ?????? )= ?????? ?????? ( ?????? ) ≥ ??????Javob: va 22) tenglamani yeching. ⟺ [ ?????? = − ?????? { [ ?????? = − ?????? ?????? = ?????? ?????? ≥ − ?????? ⟺ [ ?????? = − ?????? ?????? = ?????? [ ?????? + ?????? = ?????? { ?????? ?????? + ?????? ?????? − ???????????? = ?????? ?????? + ?????? ≥ ?????? IRRATSIONAL TENGLAMALAR Javob: va 53) ⟺ [ ?????? ?????? − ?????? ?????? + ?????? = ?????? { ?????? = ?????? ?????? ≤ ?????? ; ?????? ≥ ?????? [ √ ?????? ?????? − ?????? ?????? + ?????? − 2 = ?????? { ?????? − ?????? = ?????? ?????? ?????? − ?????? ?????? + ?????? ≥ ?????? ( ?????? − ?????? )( √ ?????? ?????? − ?????? ?????? + ?????? − ?????? )= ?????? ?????? ?????? − ?????? ?????? = ?????? ?????? ?????? = ?????? ; ?????? ?????? = ?????? MISOLLAR YECHISH ?????????????????????????????????????????? : ( ?????? − ?????? ) √ ?????? ?????? − ?????? ?????? + ?????? = ?????? ( ?????? − ?????? ) ?????? √ ?????? ( ?????? ) = ?????? √ ?????? ( ?????? )Javob: va 1 tenglamani yeching ?????????????????????????????????????????? : ?????? ?????? + ?????? ?????? − ?????? = ?????? ?????? − ?????? toq son bo‘lsa, ?????? ?????? + ?????? ?????? − ?????? = ?????? ?????? ?????? = − ?????? ; ?????? ?????? = ?????? IRRATSIONAL TENGLAMALAR ?????? √ ?????? ( ?????? ) = ?????? √ ?????? ( ?????? )Javob: 5) ?????????????????????????????????????????? : { ?????? ?????? − ?????? = ?????? ?????? ≥ ?????? yoki ?????? = ?????? ⟺ { [ ?????? = − ?????? ?????? = ?????? ?????? ≥ ??????IRRATSIONAL TENGLAMALAR juft son bo‘lsa, 6) Tenglamani yeching. ?????? ¿ √ ???????????? ?????? + ?????? = − ???????????? ⟹ − ???????????? < ?????? ⟹ ?????? ∈ ∅ ?????? ¿ √ ?????? ?????? + ?????? = − ?????? ⟹ − ?????? < ?????? ⟹ ?????? ∈ ∅MISOLLAR YECHISH √ ?????? ?????? − ?????? ?????? + ?????? = ?????? + ??????7) Tenglamani yeching. ⟺ { ?????? ?????? − ?????? ?????? + ?????? = ( ?????? + ?????? ) ?????? ?????? + ?????? ≥ ?????? ⟺ { ?????? ?????? − ?????? ?????? + ?????? = ?????? ?????? + ?????? ?????? + ?????? ?????? ≥ − ?????? ⟺ { − ?????? ?????? = ?????? ?????? ≥ − ?????? ⟺ { ?????? = − ?????? ?????? ?????? ≥ − ?????? Javob:MISOLLAR YECHISH √ ?????? ?????? + ?????? ?????? + ?????? = ?????? + ??????8) Tenglamani yeching. ⟺ { ?????? ?????? + ?????? ?????? + ?????? = ( ?????? + ?????? ) ?????? ?????? + ?????? ≥ ?????? ⟺ { ?????? ?????? + ?????? ?????? + ?????? = ?????? ?????? + ?????? ?????? + ???????????? ?????? ≥ − ?????? ⟺ { − ?????? ?????? = ???????????? ?????? ≥ − ?????? ⟺ { ?????? = − ???????????? ?????? ?????? ≥ − ?????? Javob: MISOLLAR YECHISH √ ?????? ?????? + ?????? ?????? − ?????? = √ − ?????? ?????? − ??????9) Tenglamani yeching. Y ???????????????????????????????????? : { ?????? ?????? + ?????? ?????? − ?????? = − ?????? ?????? − ?????? − ?????? ?????? − ?????? ≥ ?????? ⟺ { ?????? ?????? − ?????? ?????? − ?????? = ?????? ?????? ≤ − ?????? ?????? ⟺ { [ ?????? ?????? = ?????? − √ ???????????? ?????? ?????? ?????? = ?????? + √ ???????????? ?????? ?????? ≤ − ?????? ?????? Javob: MISOLLAR YECHISH √ − ?????? ?????? ?????? − ?????? ?????? − ?????? = √ ?????? + ??????10) Tenglamani yeching. ?????????????????????????????????????????? : { − ?????? ?????? ?????? − ?????? ?????? − ?????? = ?????? + ?????? ?????? + ?????? ≥ ?????? ⟺ { − ?????? ?????? ?????? − ?????? ?????? − ?????? = ?????? ?????? ≥ − ?????? ⟺ { ?????? = ???????????? − ???????????? = − ?????? < ?????? Javob: MISOLLAR YECHISH ?????????????????????????????????????????? : ?????? ( ?????? )√ ?????? ( ?????? )= ?????? ⟺ [ ?????? ( ?????? )= ?????? { ?????? ( ?????? )= ?????? ?????? ( ?????? ) ≥ ??????Javob: 2 ta11) tenglama nechta haqiqiy ildizga ega? ⟺ [ − ?????? ?????? ?????? + ?????? ?????? + ???????????? = ?????? { ?????? ?????? − ?????? = ?????? − ?????? ?????? ?????? + ?????? ?????? + ???????????? ≥ ?????? MISOLLAR YECHISH ?????????????????????????????????????????? : ?????? ( ?????? )√ ?????? ( ?????? )= ?????? ⟺ [ ?????? ( ?????? )= ?????? { ?????? ( ?????? )= ?????? ?????? ( ?????? ) ≥ ??????Javob: 12) tenglamaning haqiqiy ildizlari yig‘indisini toping. ?????? = ?????? ??????MISOLLAR YECHISH Darslikning 68- betidagi 11, 13, 15- mashqlarMUSTAQIL YECHISH UCHUN TOPSHIRIQ E’TIBORINGIZ UCHUN RAHMAT

SODDA IRRATSIONAL TENGLAMALAR

O‘zgaruvchisi ildiz ostida qatnashgan tenglama irratsional tenglamalar deyiladi.√ ???????????? ?????? − ???????????? = ???????????? √ ?????? ?????? − ?????? ?????? + ?????? = ?????? + ?????? √ ?????? ?????? + ?????? ?????? − ?????? = √ − ?????? ?????? − ?????? ( ?????? ?????? + ?????? ?????? + ?????? ) √ ?????? + ?????? = ?????? SODDA IRRATSIONAL TENGLAMALAR

√ ?????? ( ?????? ) = ?????? ( ?????? ) ⟺ { ?????? ( ?????? ) ≥ ?????? ?????? ( ?????? ) = ?????? ?????? ( ?????? ) √ ?????? ( ?????? ) = ?????? , ?????? < ?????? ⟹ ?????? ∈ ∅ √ ?????? ( ?????? ) = ?????? , ?????? ≥ ?????? ⟹ ?????? ( ?????? ) = ?????? ?????? ?????? ?????? √ ?????? ( ?????? ) = ?????? ( ?????? ) ⟺ { ?????? ( ?????? ) ≥ ?????? ?????? ( ?????? ) = ?????? ?????? ?????? ( ?????? )IRRATSIONAL TENGLAMALAR

Javob: tenglamani yeching.?????? = ?????? ?????????????????????????????????????????? : √ ?????? ( ?????? ) = ?????? ( ?????? ) ⟺ { ?????? ( ?????? ) ≥ ?????? ?????? ( ?????? )= ?????? ?????? ( ?????? ) { ?????? − ?????? ≥ ?????? ?????? + ?????? ?????? − ?????? ?????? = ?????? ?????? − ?????? ?????? + ?????? { ?????? ≥ ?????? ?????? ?????? ?????? − ?????? ?????? = ?????? { ?????? ≥ ?????? [ ?????? = ?????? ?????? = ?????? MISOLLAR YECHISH

?????????????????????????????????????????? : ?????? ( ?????? ) √ ?????? ( ?????? ) = ?????? ⟺ [ ?????? (?????? )= ?????? { ?????? ( ?????? )= ?????? ?????? ( ?????? ) ≥ ??????Javob: va 22) tenglamani yeching. ⟺ [ ?????? = − ?????? { [ ?????? = − ?????? ?????? = ?????? ?????? ≥ − ?????? ⟺ [ ?????? = − ?????? ?????? = ?????? [ ?????? + ?????? = ?????? { ?????? ?????? + ?????? ?????? − ???????????? = ?????? ?????? + ?????? ≥ ?????? IRRATSIONAL TENGLAMALAR

O'xshashlar

Irratsional tenglamalar
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Logarifmik tenglamalar
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