Question

chứng minh 2x⁸+2x⁷+1 > 0 với mọi x 

Answer 1

Ta xet 3 truong hop

TH1 : x la so nguyen duong 

Co 2x^8 + 2x^7 + 1 = duong + duong + duong = duong

Ma so duong luon lon hon 0

=> 2x^8 + 2x^7 + 1 > 0 voi x la so nguyen duong

TH2 : x la so nguyen am

Co 2x^8 + 2x^7 + 1 = duong + am + duong .

Do 2x^8 > 2x^7 nen tong tren mang dau duong

Ma so duong luon lon hon 0

=> 2x^8 + 2x^7 + 1 > 0 voi x la so nguyen am

TH3 : x = 0 

Voi x = 0 ta co 2x^8 + 2x^7 + 1 = 0 + 0 + 1 = 1

Ma 1 > 0 

=> 2x^8 + 2x^7 + 1 > 0 voi x = 0 

Vay 2x^8 + 2x^7 + 1 > 0 voi moi x