(14) Kesen Teoremleri

Kenarortay teoremi:

2 V_{a}^{2} = b^{2} + c^{2} - (\frac{a^{2}}{2})

\Rightarrow 2 n^{2} = n^{2} + 4 + 4 n + n^{2} + 1 - 2 n - \frac{36}{2}

2 n = 18 - 5

n = \frac{13}{2}

Birinci yol:

Kosinüs teoremi:

c^{2} = a^{2} - 2 a b \cos C

\Rightarrow 20 = 25 + 10 - 2 \times 5 \times \sqrt{10} \cos C

\Rightarrow x^{2} = 4 + 10 - 2 \times 2 \times \sqrt{10} \cos C

= 14 - 2 \times 2 \times \sqrt{10} \cos C \times \frac{5}{5}

= 14 - \frac{2}{5} \times 15

= 8

\Rightarrow x = 2 \sqrt{2}

İkinci yol:

Stewart Teoremi:

x^{2} = (\frac{b^{2} m + c^{2} n}{m + n}) - m n

\Rightarrow x^{2} = (\frac{10 \times 3 + 20 \times 2}{5}) - 6

= 8

\Rightarrow x = 2 \sqrt{2}

Birinci yol:

p^{2} + 36 = q^{2} + 25

q^{2} + 9 = r^{2} + 4

r^{2} + 16 = p^{2} + x^{2}

\Rightarrow 61 = 29 + x^{2}

\Rightarrow x = 4 \sqrt{2}

İkinci yol:

Carnot teoremi:

a^{2} + c^{2} + e^{2} = b^{2} + d^{2} + f^{2}

\Rightarrow 4 + x^{2} + 25 = 16 + 36 + 9

x = 4 \sqrt{2}

| 3 x - 21 | < 4 x < 3 x + 15

3 x - 21 < 4 x < 3 x + 15

\Rightarrow - 21 < x < 15

21 - 3 x < 4 x < 3 x + 15

\Rightarrow 3 < x < \frac{6 x + 15}{7}

\Rightarrow 3 < x < 15

Neoturanism