間違った平方根の和
解説
\sqrt{ka^2} + \sqrt{kb^2} - \sqrt{kc^2} - \sqrt{kd^2}
= a\sqrt{k} + b\sqrt{k} - c\sqrt{k} - d\sqrt{k}
= (a + b - c - d)\sqrt{k}
= \sqrt{k(a + b - c - d)^2}
というわけで (\pm a \pm b \pm c \pm d)^2 = \pm a^2 \pm b^2 \pm c^2 \pm d^2であるような数を見つければいい
kは飾り
:+sqrt(1) + sqrt(4) - sqrt(16) + sqrt(36) = sqrt(+1 + 4 - 16 + 36)
+sqrt(1) + sqrt(4) - sqrt(25) + sqrt(36) = sqrt(+1 + 4 - 25 + 36)
+sqrt(1) + sqrt(9) - sqrt(25) + sqrt(64) = sqrt(+1 + 9 - 25 + 64)
+sqrt(1) + sqrt(9) - sqrt(49) + sqrt(64) = sqrt(+1 + 9 - 49 + 64)
+sqrt(1) + sqrt(16) - sqrt(49) + sqrt(81) = sqrt(+1 + 16 - 49 + 81)
-sqrt(1) - sqrt(4) + sqrt(16) + sqrt(25) = sqrt(-1 - 4 + 16 + 25)
-sqrt(1) - sqrt(9) + sqrt(25) + sqrt(49) = sqrt(-1 - 9 + 25 + 49)
-sqrt(1) + sqrt(16) + sqrt(25) - sqrt(36) = sqrt(-1 + 16 + 25 - 36)
-sqrt(1) - sqrt(16) + sqrt(36) + sqrt(81) = sqrt(-1 - 16 + 36 + 81)
-sqrt(1) + sqrt(25) + sqrt(49) - sqrt(64) = sqrt(-1 + 25 + 49 - 64)
-sqrt(4) - sqrt(9) + sqrt(49) + sqrt(64) = sqrt(-4 - 9 + 49 + 64)
-sqrt(4) + sqrt(16) + sqrt(25) - sqrt(36) = sqrt(-4 + 16 + 25 - 36)
-sqrt(4) + sqrt(25) + sqrt(64) - sqrt(81) = sqrt(-4 + 25 + 64 - 81)
-sqrt(9) + sqrt(25) + sqrt(49) - sqrt(64) = sqrt(-9 + 25 + 49 - 64)8重forループ
pythonN = 10
for a in range(1, N):
for sa in [1, -1]:
for b in range(a + 1, N):
for sb in [1, -1]:
for c in range(b + 1, N):
for sc in [1, -1]:
for d in range(c + 1, N):
for sd in [1, -1]:
x = sa * a + sb * b + sc * c + sd * d
if x <= 0:
continue
a2 = a ** 2
b2 = b ** 2
c2 = c ** 2
d2 = d ** 2
x2 = sa * a2 + sb * b2 + sc * c2 + sd * d2
def pm(x):
return "+" if x > 0 else "-"
if x * x == x2:
print(
f"{pm(sa)}sqrt({a2}) {pm(sb)} sqrt({b2}) {pm(sc)} sqrt({c2}) {pm(sd)} sqrt({d2})"
f" = sqrt({pm(sa)}{a2} {pm(sb)} {b2} {pm(sc)} {c2} {pm(sd)} {d2})"
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