Մաթեմատիկա

Առաջադրանք.38Ա) (√2)15 > (√2)9Բ) (1,5)-12 > (1,5)-29Գ) (4/π)3 > 1Դ) (2/3)4 < (2/3)8Ե) (√15/4)-7 < (√15/4)3Զ) (3/π)9 < 1Առաջադրանք.39Ա) 3√12 x (3√12)2 = √12 x (√12)2 = (3√12)1 x (3√12)2 = (√12)1+2 = (3√123) = 12Բ) (√13)5/√13 = (4√13/√13)5 = 4√134 = 132 = 169Գ) (√8)3 x (4√8)9 = (4√8)3+9 = (4√8)12 = 83 = 512Առաջադրանք.46Ա)4√3 – 2√2 | 3<2, 2<4Բ) 4√4 – 6√6 | 43>62, 64>36Գ) √3√2 – √5 | √3√2<√5, 4,24264<5Դ) 3√52 – 5√53 | √52 15>√53, (52)5>(√53)3, 510>59, 10>9Ե) √5 – 3√5 | √5>3√5, 53>52, 3>2Զ) 4√0,7 – 6√0,7 | 0,73>0,72Է) √1,1 – 11 | √11/√10<1,1, √110/10<1,1, 1,04881<11Ը) 3√0,1 – 0,1 | 3√1/10>0,1, 3√100/10>0,1, 0,464159>0,1Առաջադրանք.47Ա) √2 x √8 = √2×8 = √16 = 4Բ) √24 x √54 = √24×54 = √1296 = 36Գ) √3 x 3√3 x 6√3 = 6√33 x 6√3x 6√3 = 6√33 x 32 x 3 = 6√36 = 3Դ) 6√16 x 3√4 x √64 = 18√46+6+6 = 18√46 x 18√642 = 18√163 x 46 x 642 = 18√46+6+6 = 18√4+8 = 4Առաջադրանք.48Ա) √18/√2 = √2 x √9/√2 = √9 = 3Բ) √162/√18 = √18√9 = √9 = 3Առաջադրանք.54Ա) x1/4 ∙ x3/10 = x1/4 + 3/10 = x11/20 = 20√xԲ) a=-3/8 : a1/4 = 1/a2/8 ∙ 1/a1/4 = 13/8 : 1/a1/4 = 13/8+1/4 = 1/a5/8 = 1/8√a5 = 1/8√a5 ∙ 8√a3/8√a3 = 9√a3/√a5∙a3 = 8√a3/aԳ) (y 3/4)4/5 = y3/2 ∙ 4/3 = y1/2 = √yԴ) (x 2/3)0,6 ∙ x2/5 = x2/3 ∙ 0,6 ∙ x2/5 = x2/5 ∙ x2/5 = x4/5 = 5√x4Առաջադրանք.58Ա) (31/30)1,13 > 1Բ) (1,0001)0,0001 > 1Գ) (27/26)0,14 > 1Դ) (π/3)-0,037 < 1Ե) (√0,3)1,89 < 1Զ) (9√0,999)999 < 1Է) (1/143)0 = 1Ը) 00,023 < 1Առաջադրանք.61Ա) (5√3)√3 = 5√3 ∙ √3 = 53 = 125Բ) ((√2)√2)√2 = √2√2∙√2 = √22Առաջադրանք.63Ա) 3√5 – 93√5 > 32√5 > 2√52 > 25 > 4Բ) (2/3)√2 – 8/27√7<37<9Գ) 7–π – 11/7<10,0022<1Դ) (0,5)–√2 – 1(1/2)–√2 > 12,67 > 1Ե) (0,2)–√3 – 55√3 > 51√3 > 1Զ) (4/3)π – 9/16(4/3)π < (4/3)-4-π < 2Առաջադրանք.64Բ) (1,8)n < (1,8)√7 < (1,8)n+1n=2Գ) (3/4)n < (3/4)√6 < (3/4)n-1n=3Առաջադրանք.65Ա) 9x+1 = 91+x ∙ 9^ = 9 ∙ 9xԲ) (0,5)x-3 = (0,5)x ∙ (0,5)3 = (0,5)x