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1 ) 8 (3^n ) -5 ( 3^n-1)/ 開方 9^n +3^n-2 ANS 57/102 ) solve the simultaneous eduations {5p+8q =57 p-10q=-35 ans p=5 q= 4 2b ) hence solve 5x+1 +2 ^y+3 =57 5^x-1 -2 ^y+1 =-7 x= 1 y=23 consider that x-z ^3 =0 and x^3 -y^2 =0 find logx :log y :log z ANs 6:9:2if... 顯示更多 1 ) 8 (3^n ) -5 ( 3^n-1)/ 開方 9^n +3^n-2 ANS 57/10 2 ) solve the simultaneous eduations {5p+8q =57 p-10q=-35 ans p=5 q= 4 2b ) hence solve 5x+1 +2 ^y+3 =57 5^x-1 -2 ^y+1 =-7 x= 1 y=2 3 consider that x-z ^3 =0 and x^3 -y^2 =0 find logx :log y :log z ANs 6:9:2 if y=2xz find the values of x y z ans x= 64 y =512 z = 4

最佳解答:

Ans 1 : 8 (3^n ) -5 ( 3^n-1)/ √9^n +3^n-2 = 8(3^n) – 5 (3^n)(3^-1) / 3^n +3^n(3^-2) = 8(3^n) –5 (3^n)(1/3) / 3^n +3^n(1/9) = 8(3^n) –5/3 (3^n) / 3^n (1+1/9) = 3^n(8 –5/3) / 3^n (1+1/9) = 19/3 / 10/9 = 19/3 * 9/10 = 57/10 ans 2: 5p+8q =57 p-10q=-35 if p-10q = -35 p=-35 +10q so 5p+8q =57 5(-35+10q) +8q = 57 -175+ 50q + 8q = 57 58q = 57+175 58q = 232 q = 4 then p= -35+10q p= -35+10 (4) p= 5 2b ) 5x+1 +2 ^y+3 =57 5^x-1 -2 ^y+1 =-7 ans 2b): 5^x+1 +2 ^y+3 =57 5(5^x) +2^3(2^y) =57 5(5^x) +8(2^y) =57 Let p=5^x , q=2^y Then 5p+8q=57 And 5^x-1 -2 ^y+1 =-7 5^x (5^-1) – 2^y(2) =7 5^x (1/5) – 2^y(2) =7 Let p=5^x , q=2^y p/5 – 2q =-7 p-10q = -35 so put the equation to question 2 p=5 , q=4 (we had proven before) p=5^x 5=5^x x =1 q=2^y 4=2^y y=2 ans 3: x-z ^3 =0 x= z^3 x^3 -y^2 =0 x^3 = y^2 if x= z^3 so (z^3)^3 = y^2 z^9 =y^2 then x^3=y^2=z^9 and 3 log x= 2 log y = 9 log z let this equation over 18 (因18是3,2,9之最小公倍數) log x/6 = log y/9 = log z /2 so log x : log y : log z = 6 : 9 : 2 if y=2xz find the values of x y z ans: y=2xz because x^3 = y^2 =z^9 so y^2= (2xz)^2 x^3 =4 (x^2)(z^2) x =4 z^2 and x^3= z^9 (4z^2)^3 = z^9 64 (z^6) = z^9 64 = z^3 z = 4 and x^3 = z^9 x^3 = 4^9 x^3 = 64^3 x = 64 and y = 2xz y = 2(64)(4) y = 512

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