1 College math competitions ranking Let a,b,c,d be real numbers which are strictly positive.Show that 1<a/(a+b+c)+b/(b+a+d)+c/(c+a+d)+d/(d+c+b)<2. I need help please.

firmezas1

firmezas1

Answered question

2022-09-06

1 College math competitions ranking
Let a , b , c , d be real numbers which are strictly positive.
Show that
1 < a a + b + c + b b + a + d + c c + a + d + d d + c + b < 2.
I need help please.

Answer & Explanation

Mario Monroe

Mario Monroe

Beginner2022-09-07Added 12 answers

No advanced techniques are necessary, just observe that
a a + b + c + d < a a + b + c < a a + b .
Dangelo Rosario

Dangelo Rosario

Beginner2022-09-08Added 3 answers

Because 1 = c y c a a + b + c + d < c y c a a + b + c < c y c a + d a + b + c + d = 2

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