Tentukan nilai dari,.... Question from @RiaAyuN

October 2018 2 17 Report

Tentukan nilai dari, $\sqrt{2+ \sqrt{2+ \sqrt{2+ \sqrt{2+ \sqrt{2+ \sqrt{2+ \sqrt{...} } } } } } }$

hendrisyafa Jika :

$y= \sqrt{2+ \sqrt{2+ \sqrt{2}... } }$

kuadratkan ruas kiri dan kanan

$y^{2}=2+ \sqrt{2+ \sqrt{2+ \sqrt{2...} } }$

$y^{2} =2+y$

y² - y - 2 = 0
(y + 1 ) (y - 2) = 0
y+1 = 0 dan y - 2 = 0
y = -1 y = 2

sehingga :

$\sqrt{2+ \sqrt{2+ \sqrt{2}... } } =2$

1 votes Thanks 0

ImmanuelSinaga Misalkan :

$\boxed{\boxed{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+.......}}}}}}~~=~~x}}$

Kuadratkan kedua ruas :

$\left(\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+.......}}\right)^2~~=~~x^2$

Didapat :

$2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+.......}}}}}~=~x^2 \\ \\ \text{Ubah~kembali~menjadi~x}~: \\ 2~+~x~~=~~x^2 \\ \\ \text{Faktorkan~~:} \\ \\ 0~~=~~x^2-x-2 \\ 0~~=~~(x-2)(x+1) \\ x~=~2~~~\boxed{\text{Bernilai positif }} \\ x~=~-1~~\boxed{\text{Tidak~mungkin~bernilai~negatif}} \\ \\$

Maka :

$\boxed{\boxed{\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+\sqrt{2+.......}}}}}}~~~=~~~2}}$

1 votes Thanks 1

About Us

Life Enjoy

" Life is not a problem to be solved but a reality to be experienced! "

Apa manfaat bersaudara dalam islam?

Diketahui log 2 = 0,3010 , log 3 = 0,4771 dan log 7 = 8451. tentukan log 21. dan

Selesaikan,

Hasil dari,

Selesaikan soal berikut,

Jika , tentukan nilai a dan b.

Recommend Questions

Life Enjoy

Get in touch

Social