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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 (a^6+a^4+a^2+1)/a^3 → (a^3 (a^3+a+1/a+1/a^3 ))/a^3 = a^3+a+1/a+1/a^3 = (a^3+1/a^3 ) + (a+1/a) a+1/a = 4 On cubing both sides, (a+1/a)^3 = (4)^3 a^3+1/a^3 + 3 × a×1/a (4) = 64 a^3+1/a^3 + 12 = 64 a^3+1/a^3 = 52 Therefore, a^3+1/a^3 + a+1/a = 52 + 4 = 56.
128 ÷ 22 × ? = 15% of 300 ÷ 9
(√1024 + √324)% of 780 = ?% of 260
∛21952 × 44 = ? × 14
154 × 7 + 480 × 5 = ?% of 6956
[(1245 ÷ 9) ÷ 12] × 540 = ?2 – 175
√(24 × 5 ÷ ?) × 4 = 56 + 34 – 10
Find the simplified value of the given expression.
(1/4) of {64 - 28 x 15 + 13 x 16 - 12.5 of 122}
[(√ 529) + 67] x 5 = ?
? % of 1200 = 20% of 30% of 3600
1220 ÷ 61 ÷ 5 + 450 of 20% - 70 = √ ?