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X4L
@X4L
February 2022
1
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Сравните выражения:
(Корень из 3 - 1)^3-(корень из 3 + 1)^3 и (-8)^2*2^7+(-0,1)^-1
^-значок степени
Ответ должен получаються,что оба выражения равны
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skvrttt
(√3 – 1)³ – (√3 + 1)³ и (–8)² × 2⁷ + (–0,1)⁻¹
1. (√3 – 1)³ – (√3 + 1)³ = (1,73 – 1)³ – (1,73 + 1)³ = 0,73³ – 2,73³ = (0,73 – 2,73)(0,73² + 0,73 × 2,73 + 2,73²) = –2 × (0,5329 + 1,9929 + 7,4529) = –2 × 9,9787 = –19,9574;
2. (–8)² × 2⁷ + (–0,1)⁻¹ = 64 × 2⁷ + (–0,1)⁻¹ = 2⁶ × 2⁷ + (–0,1)⁻¹ = 2¹³ + (
)¹ = 2¹³ + (–10) = 2¹³ – 10 = 8192 –
10 = 8182;
(√3 – 1
)³ – (√3 + 1)³ и (–8)² × 2⁷ + (–0,1)⁻¹ —>
–19,9574 и 8182
—>
–19,9574 <
8182
3 votes
Thanks 1
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Answers & Comments
1. (√3 – 1)³ – (√3 + 1)³ = (1,73 – 1)³ – (1,73 + 1)³ = 0,73³ – 2,73³ = (0,73 – 2,73)(0,73² + 0,73 × 2,73 + 2,73²) = –2 × (0,5329 + 1,9929 + 7,4529) = –2 × 9,9787 = –19,9574;
2. (–8)² × 2⁷ + (–0,1)⁻¹ = 64 × 2⁷ + (–0,1)⁻¹ = 2⁶ × 2⁷ + (–0,1)⁻¹ = 2¹³ + ()¹ = 2¹³ + (–10) = 2¹³ – 10 = 8192 – 10 = 8182;
(√3 – 1)³ – (√3 + 1)³ и (–8)² × 2⁷ + (–0,1)⁻¹ —>
–19,9574 и 8182 —>
–19,9574 < 8182