25. Jika (2.006)^2x +1/(2.006)^2x=5 nilai(2.006)^x + (2.006)^-x = ​

Pertanyaan:

25. Jika (2.006)^2x +1/(2.006)^2x=5 nilai(2.006)^x + (2.006)^-x = ​

Jika ( 2.006 ) 2 x + 1 ( 2.006 ) 2 x = 5 open paren 2.006 close paren raised to the 2 x power plus the fraction with numerator 1 and denominator open paren 2.006 close paren raised to the 2 x power end-fraction equals 5 ( 2 . 0 0 6 ) 2 x + 1 ( 2 . 0 0 6 ) 2 x = 5 , maka nilai ( 2.006 ) x + ( 2.006 ) − x open paren 2.006 close paren to the x-th power plus open paren 2.006 close paren raised to the negative x power ( 2 . 0 0 6 ) x + ( 2 . 0 0 6 ) − x adalah 7 the square root of 7 end-root 7 √ , karena kita bisa memisalkan y = ( 2.006 ) x y equals open paren 2.006 close paren to the x-th power y = ( 2 . 0 0 6 ) x , sehingga y 2 + 1 y 2 = 5 y squared plus the fraction with numerator 1 and denominator y squared end-fraction equals 5 y 2 + 1 y 2 = 5 , lalu kita cari y + 1 y y plus 1 over y end-fraction y + 1 y dengan menggunakan rumus ( y + 1 y ) 2 = y 2 + 2 + 1 y 2 open paren y plus 1 over y end-fraction close paren squared equals y squared plus 2 plus the fraction with numerator 1 and denominator y squared end-fraction ( y + 1 y ) 2 = y 2 + 2 + 1 y 2 , sehingga ( y + 1 y ) 2 = 5 + 2 = 7 open paren y plus 1 over y end-fraction close paren squared equals 5 plus 2 equals 7 ( y + 1 y ) 2 = 5 + 2 = 7 , maka y + 1 y = 7 y plus 1 over y end-fraction equals the square root of 7 end-root y + 1 y = 7 √ .

Langkah-langkah Penyelesaian:

Jadi, nilai ( 2.006 ) x + ( 2.006 ) − x = 7 open paren 2.006 close paren to the x-th power plus open paren 2.006 close paren raised to the negative x power equals the square root of 7 end-root ( 2 . 0 0 6 ) x + ( 2 . 0 0 6 ) − x = 7 √ .