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Avur1
@Avur1
July 2022
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докажите тождество.√(34+24√2)=4+3√2
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dbalakireva8
4-3*√2)²=16-24*√2+18=34-24*√2
Тогда √(34-24√2)=3*√2-4
Следовательно
(4-3√2)²+8√(34-24√2)-2=34-24*√2+24*√2-32-2=0
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MaxikMK
Подгоняем подкоренное выражение под формулу: a² + b² = 2ab.
34 = a² + b²,
24√2 = 2ab.
√(34 + 24√2) = √(4² + (3√2)² + 2*4*3√2) = √(4+3√2)² = 4 + 3√2.
Ч. т. д.
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Answers & Comments
Тогда √(34-24√2)=3*√2-4
Следовательно
(4-3√2)²+8√(34-24√2)-2=34-24*√2+24*√2-32-2=0
34 = a² + b²,
24√2 = 2ab.
√(34 + 24√2) = √(4² + (3√2)² + 2*4*3√2) = √(4+3√2)² = 4 + 3√2.
Ч. т. д.