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nazivinchik
@nazivinchik
July 2022
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Помогите найти значения выражений.
[tex]1) (\sqrt13+\sqrt7)^2/10+\sqrt91
2) 5* \sqrt[3]{9}- \sqrt[6]{9}
3)( \sqrt[3]{49} * \sqrt[6]{49})
4)(\sqrt{15}- \sqrt{60}) * \sqrt{15}
5) (8 \sqrt{3})^2/8 [/tex](sqrt13+sqrt7)^2/10+sqrt91
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nKrynka
Решение
1) (√13 + √7)² /(10 + √91) = (13 + 2√91 + 7)/(10 + √91) =
= (20 + 2√91)/(10 + √91) = [2*(10 + √91) / (10 + √91) = 2
2) 5*9¹/³ - 9¹/⁶ = 5*3²/³ - 3¹/³ = 5*√3*(√3-1) = 15 - 5√3
3) (49¹/³ * 49¹/³) = 7²/³ * 7¹/³ = 7
4) (√15 - √60)*√15 = 15 - 2*15 = - 15
5) (8√3)² / 8 = (64*3)*8 = 24
2 votes
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Answers & Comments
1) (√13 + √7)² /(10 + √91) = (13 + 2√91 + 7)/(10 + √91) =
= (20 + 2√91)/(10 + √91) = [2*(10 + √91) / (10 + √91) = 2
2) 5*9¹/³ - 9¹/⁶ = 5*3²/³ - 3¹/³ = 5*√3*(√3-1) = 15 - 5√3
3) (49¹/³ * 49¹/³) = 7²/³ * 7¹/³ = 7
4) (√15 - √60)*√15 = 15 - 2*15 = - 15
5) (8√3)² / 8 = (64*3)*8 = 24