_7(3x+5)+√_7^2(2x+5)=0 tenglama nechta haqiqiy ildizga ega?

Aniqlanish sohasi $x>-\frac53$, unda $2x+5>1$, demak $\sqrt{\log_7^2(2x+5)}=\log_7(2x+5)$. Tenglama $\log_7\left((3x+5)(2x+5)\right)=0$, ya’ni $6x^2+25x+24=0$: $x=-\frac32$ yoki $x=-\frac83$. Sohaga faqat $x=-\frac32$ tegishli, ildiz bitta.

Manba: UZBMB namunaviy test topshiriqlari (Milliy sertifikat, Matematika)