Toán Lớp 7: 32^x.16^x=1024 (X-5)^2=(1-3x)^2

Question

Toán Lớp 7:  32^x.16^x=1024 (X-5)^2=(1-3x)^2

minhhaanh · Answer

Giải đáp:   $  $   1,   32^x &times; 16^x=1024   -> (2^5)^x &times; (2^4)^x=1024   -> 2^{5x} &times; 2^{4x} = 1024   -> 2^{5x+4x}=1024   -> 2^{9x} = 2^{10}   -> 9x=10   ->x=10&divide;9   ->x=10/9   Vậy x=10/9   2,   (x-5)^2 = (1-3x)^2 (1)   X&eacute;t : (x-5)^2   = (x-5)(x-5)   =x (x-5) -5 (x-5)   =x^2-5x-5x+25   = x^2-10x+25 (2)   X&eacute;t : (1-3x)^2   = (1-3x) (1-3x)   = 1 (1-3x) -3x (1-3x)   = 1 -3x - 3x + 9x^2   = 9x^2 - 6x + 1 (3)   Tahy (2), (3) v&agrave;o (1) ta được :   -> x^2 - 10x + 25 = 9x^2 - 6x + 1   -> x^2 - 10x +25 - 9x^2 + 6x -1=0   -> (x^2-9x^2) + (-10x+6x) + (25-1)=0   -> -8x^2 - 4x +24=0   -> - 4 (2x^2 + x - 6)=0   -> 2x^2 +x-6=0   -> 2x^2 + 4x - 3x - 6=0   -> (2x^2+4x) - (3x+6)=0   -> 2x (x + 2) - 3 (x + 2)=0   -> (x+2) (2x-3)=0   ->x+2=0 hoặc 2x-3=0   -> x=-2 hoặc 2x=3   ->x=-2 hoặc x=3/2   Vậy x=-2 hoặc x=3/2

hongocha12 · Answer

Giải đáp:       Lời giải và giải thích chi tiết:   32^x * 16^x = 1024   -> 512^x = 1024   -> (2^9)^x = 1024   -> 2^{9x} = 2^10   -> 9x = 10   -> x = 10/9   Vậy x  in {10/9}   (x-5)^2 = (1-3x)^2   -> x^2 - 10x + 25 = 1 - 6x + 9x^2   -> x^2 - 10x + 25 - 1 + 6x - 9x^2 = 0   -> -8x^2 - 4x + 24 = 0   -> 2x^2 + x - 6 = 0   -> 2x(x+2) - 3(x+2) = 0   -> (x+2)(2x-3) = 0   -> ( left[  begin{array}{l}x+2=0  2x-3=0 end{array}  right. )    -> ( left[  begin{array}{l}x=-2  x= dfrac{3}2 end{array}  right. )    Vậy x  in {-2,3/2}