Question

Jika x+y+z = a dan 1/x+1/y+1/z=1/a, maka nilai xyz (dibaca x kali y kali z) sama dengan.... (jawaban dinyatakan dalam a, misalnya 4a, 9a, dsb.)

Answer 1

Jawabannya liat di gambar ya...

Answer 2

(1/x + 1/y + 1/z)(x + y + z) = 3 + (y + z)/x + (x + z)/y + (x + y)/z
1/a * a = 3 + [yz(y + z) + xz(x + z) + xy(x + y)]/xyz
1 = 3 + [(y²z + yz² + x²z + x²z + xz² + x²y + xy²)]/xyz
-2xyz = (x²(y + z) + y²(x + z) + z²(x + y)]
-2xyz = x²(a - x) + y²(a - y) + z²(a - z)
-2xyz = ax² + ay² + az² - (x³ + y³ + z³)
-2xyz = a(x² + y² + z²) - ((x + y + z)(x² + y² + z²))

cari x² + y² + z² = (x + y + z)² - 2(xy + xz + yz)