Question Number 149469 by mathdanisur last updated on 05/Aug/21

Compare: 1900^(3/4) + 99^(3/4) and 1999^(3/4)

Answered by mindispower last updated on 05/Aug/21

f(x)=x^(3/4) +(1−x)^(3/4) ,x∈[0,1[,f(1−x)=f(x) f′(x)=(3/4)((1/x^(1/4) )−(1/((1−x)^(1/4) )))=(3/4)((((1−x)^(1/4) −x^(1/4) )/((x(1−x))^(1/4) ))) if x≤(1/2),f′>0 if x∈](1/2),1[ f′<0 f(1)=f(0)=1 ⇒∀x∈[0,1] f(x)≥1 for x=((1900)/(1999)) f(((1900)/(1999)))=(((1900)/(1999)))^(3/4) +(1−((1900)/(1999)))^(3/4) ≥1 ⇒(1900)^(3/4) +99^(3/4) ≥1999^(3/4)

Commented bymathdanisur last updated on 05/Aug/21

Thank You Ser Cool

Commented bymathdanisur last updated on 06/Aug/21

Ser, can it be written as Newton′s Binomial or inequality.?