jika x^1/2+x^-1/2=3,maka x+x^-1 adalah....?
Matematika
Orii
Pertanyaan
jika x^1/2+x^-1/2=3,maka x+x^-1 adalah....?
1 Jawaban
-
1. Jawaban hendrisyafa
Buat pemisalan :
jika [tex] x^{ \frac{1}{2} } [/tex] = p
maka
[tex] x^{- \frac{1}{2}} [/tex] = [tex] \frac{1}{p} [/tex]
Sehingga
[tex] x^{ \frac{1}{2}}[/tex] + [tex] x^{ -\frac{1}{2}} [/tex] = 3 menjadi
p + [tex] \frac{1}{p} [/tex] = 3
Maka
x+[tex] x^{-1} [/tex] = [tex] p^{2}+ \frac{1}{ p^{2} } [/tex]
= ( p + [tex] \frac{1}{p} [/tex])[tex] ^{2} [/tex] - 2 (p x [tex] \frac{1}{p} [/tex] )
= [tex] (3)^{2} [/tex] - 2 (1)
= 9-2
= 7