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Marusiait99
@Marusiait99
July 2022
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Люди добрые! Еще один кошмар, который нужно решить:
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m11m
(
a¹/²
+
a¹/²
) *
a-b
)⁴
( a¹/⁴-b¹/⁴ a¹/⁴+b¹/⁴) 2a+2a¹/²b¹/²)
1)
a¹/²
+
a¹/²
=
a¹/² (a¹/⁴+b¹/⁴) + a¹/² (a¹/⁴-b¹/⁴)
=
a¹/⁴-b¹/⁴ a¹/⁴+b¹/⁴ (a¹/⁴-b¹/⁴)(a¹/⁴+b¹/⁴)
=
a¹/²(a¹/⁴+b¹/⁴+a¹/⁴-b¹/⁴)
=
a¹/² * 2a¹/⁴
=
2 a²/⁴⁺¹/⁴
=
(a¹/⁴-b¹/⁴)(a¹/⁴+b¹/⁴) (a¹/⁴-b¹/⁴)(a¹/⁴+b¹/⁴) (a¹/⁴-b¹/⁴)(a¹/⁴+b¹/⁴)
=
2a³/⁴
=
2a³/⁴
(a¹/⁴)²-(b¹/⁴)² a¹/²-b¹/²
2)
a-b
=
(a¹/²-b¹/²)(a¹/²+b¹/²)
=
a¹/²-b¹/²
2a+2a¹/²b¹/² 2a¹/²(a¹/²+b¹/²) 2a¹/²
3)
2a³/⁴
*
a¹/²-b¹/²
=a³/⁴⁻¹/² =a³/⁴⁻²/⁴=a¹/⁴
a¹/²-b¹/² 2a¹/²
4) (a¹/⁴)⁴=a¹=a
Ответ: получится а.
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Marusiait99
Огромное спасибо! Сама бы ни за что не додумалась!
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Answers & Comments
( a¹/⁴-b¹/⁴ a¹/⁴+b¹/⁴) 2a+2a¹/²b¹/²)
1) a¹/² + a¹/² = a¹/² (a¹/⁴+b¹/⁴) + a¹/² (a¹/⁴-b¹/⁴) =
a¹/⁴-b¹/⁴ a¹/⁴+b¹/⁴ (a¹/⁴-b¹/⁴)(a¹/⁴+b¹/⁴)
= a¹/²(a¹/⁴+b¹/⁴+a¹/⁴-b¹/⁴) = a¹/² * 2a¹/⁴ = 2 a²/⁴⁺¹/⁴ =
(a¹/⁴-b¹/⁴)(a¹/⁴+b¹/⁴) (a¹/⁴-b¹/⁴)(a¹/⁴+b¹/⁴) (a¹/⁴-b¹/⁴)(a¹/⁴+b¹/⁴)
= 2a³/⁴ = 2a³/⁴
(a¹/⁴)²-(b¹/⁴)² a¹/²-b¹/²
2) a-b = (a¹/²-b¹/²)(a¹/²+b¹/²) = a¹/²-b¹/²
2a+2a¹/²b¹/² 2a¹/²(a¹/²+b¹/²) 2a¹/²
3) 2a³/⁴ * a¹/²-b¹/² =a³/⁴⁻¹/² =a³/⁴⁻²/⁴=a¹/⁴
a¹/²-b¹/² 2a¹/²
4) (a¹/⁴)⁴=a¹=a
Ответ: получится а.