14 3. Diketahui 22x + 2-2x = 119. Nilai 2*+2* adalah .... a. 13 b. 12 C. 11 d. 10 e. 9 Matematika Kelas X C
Answer (4)
The correct answer is: 29 4 − 10 i ;
To simplify the expression 2/(2+5i), multiply both the numerator and the denominator by the conjugate of the denominator, which is 2-5i, resulting in (4-10i)/29, or 4/29 - (10/29)i in component form.
To simplify the given expression 2/(2+5i), we need to eliminate the imaginary number in the denominator. To do this, we multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of 2+5i is 2-5i.
Now, let's perform the multiplication:
(2 / (2+5i)) 2-5i = (2 2-5i) / ((2+5i) (u) 2-5i)
This results in 4-10i in the numerator and 4+10i-10i+25 in the denominator. After simplification, we have (4-10i)/29.
Therefore, the simplified form of 2/(2+5i) is:
(2 / (2+5i)) = (4-10i)/29.
Which, in component form, is:
4/29 - (10/29)i
The expression 2 + 5 i 2 can be simplified to 29 4 − 10 i by multiplying both the numerator and denominator by the conjugate of the denominator. This process eliminates the imaginary part in the denominator. The final result is a complex fraction with a real and imaginary part in the numerator and a real number in the denominator.
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Jawaban:selesaikan persamaan ini untuk mencari nilai dari 2ˣ + 2⁻ˣ. Soal: Diketahui 2²ˣ + 2⁻²ˣ = 119. Nilai 2ˣ + 2⁻ˣ adalah .... a. 13b. 12c. 11d. 10e. 9 Langkah 1: Misalkan Variabel Misalkan y = 2ˣ + 2⁻ˣ Langkah 2: Kuadratkan Kedua Sisi y² = (2ˣ + 2⁻ˣ)² y² = (2ˣ)² + 2(2ˣ)(2⁻ˣ) + (2⁻ˣ)² y² = 2²ˣ + 2(2⁰) + 2⁻²ˣ y² = 2²ˣ + 2(1) + 2⁻²ˣ y² = 2²ˣ + 2⁻²ˣ + 2 Langkah 3: Substitusi dengan Persamaan yang Diketahui Kita tahu bahwa 2²ˣ + 2⁻²ˣ = 119, jadi: y² = 119 + 2 y² = 121 Langkah 4: Cari Nilai y y = √121 y = ±11 Langkah 5: Pertimbangkan Solusi Karena 2ˣ selalu positif untuk setiap nilai x, maka 2ˣ + 2⁻ˣ juga harus positif. Oleh karena itu, kita ambil solusi positif: y = 11 Jawaban: Nilai 2ˣ + 2⁻ˣ adalah 11. Pilihan Jawaban: c. 11
