Step-by-step explanation:
sqrt(8) = sqrt(4×2) = 2×sqrt(2)
so,
(a + sqrt(8))² = (a + 2×sqrt(2))² =
= a² + 4×2 + 2×a×2×sqrt(2) = a² + 8 + 4×a×sqrt(2)
so,
c = a² + 8
d = 4a
(e - 2×sqrt(3))² = f - 20×sqrt(3)
e² + 4×3 - 2×e×2×sqrt(3) = f - 20×sqrt(3)
e² + 12 - 4e×sqrt(3) = f - 20×sqrt(3)
=> we only need to compare the parts of the equation with the same factors
4e = 20
e = 5
f = e² + 12 = 5² + 12 = 25 + 12 = 37
