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In two dimensions, 2x 1 + 2x 2 is the perimeter of a rectangle with sides of length x 1 and x 2. Similarly, 4 √ x 1 x 2 is the perimeter of a square with the same area, x 1 x 2, as that rectangle. Thus for n = 2 the AM–GM inequality states that a rectangle of a given area has the smallest perimeter if that rectangle is also a square.
The first of these quadratic inequalities requires r to range in the region beyond the value of the positive root of the quadratic equation r 2 + r − 1 = 0, i.e. r > φ − 1 where φ is the golden ratio. The second quadratic inequality requires r to range between 0 and the positive root of the quadratic equation r 2 − r − 1 = 0, i.e. 0 ...
The 2023 Merdeka Tournament was the 42nd edition of the tournament which was organised by the Football Association of Malaysia. The tournament, which featured three participants, took place between 13 and 17 October. Tajikistan emerged as the champion of the tournament for their first title after beating host Malaysia 2–0 at the final. [1] [2]
Chromosome 10 is one of the 23 pairs of chromosomes in humans. People normally have two copies of this chromosome. People normally have two copies of this chromosome. Chromosome 10 spans about 134 million base pairs (the building material of DNA ) and represents between 4 and 4.5 percent of the total DNA in cells .
Because (a + 1) 2 = a, a + 1 is the unique solution of the quadratic equation x 2 + a = 0. On the other hand, the polynomial x 2 + ax + 1 is irreducible over F 4, but it splits over F 16, where it has the two roots ab and ab + a, where b is a root of x 2 + x + a in F 16. This is a special case of Artin–Schreier theory.