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a = 2 + √3 1/a = 1/(2 + √3) = 2 - √3 a + 1/a = 2 + √3 + 2 - √3 a + 1/a = 4(a6+ a4+ a2+ 1)/a3 → (a3 (a3+ a + 1/a + 1/a3))/a3 = a3 + a + 1/a + 1/a3 = (a3 + 1/a3) + (a + 1/a) a + 1/a = 4 On cubing both sides, (a + 1/a)3 = (4)3 a3 + 1/a3 + 3 × (a + 1/a ) = 64 a3+ 1/a3+ 3 × (4) = 64 a3+ 1/a3+ 12 = 64 a3+ 1/a3= 52 then, a3+ 1/a3+ a+1/a = 52 + 4 = 56
Fill in the blanks with the appropriate antonym of the word highlighted.
He was a man of _____ whereas his brother was a man of stupidity.
...1) reasons
2) logic
3) distinction
4) distinguished
5) hype
Technology is a _______ force behind progress and innovation, shaping the way we live and _______ in the modern world.
I didn’t realize how hurtful my words had been until I saw Sherrie’s expression, _________ with shock.
The deal _____________ signed while hundreds of police armed with truncheons and riot equipment remained on standby outside the hotel.