Toán Lớp 7: Tìm `x` `(2x-1)^4=81` `5^x+5^x+2=650` `(x-1)^5=-32`

Question

Toán Lớp 7:  Tìm x (2x-1)^4=81 5^x+5^x+2=650 (x-1)^5=-32

behocgioitoan · Answer

Hướng dẫn giải: a, (2x-1)^4=81 <=> (2x-1)^4=(+-3)^4 <=> ( left[ begin{array}{l}2x-1=3 2x-1=-3 end{array} right. )<=> ( left[ begin{array}{l}2x=4 2x=-2 end{array} right. )<=> ( left[ begin{array}{l}x=2 x=-1 end{array} right. ) Vậy x in{2;-1} b, 5^x+5^(x+2)=650 <=> 5^x+5^x .5^2=650 <=> 5^x(1+5^2)=650 <=> 5^x.26=650 <=> 5^x=25 <=> 5^x=5^2 <=> x=2 Vậy x=2 c, (x-1)^5=-32 <=> (x-1)^5=(-2)^5 <=> x-1=-2 <=> x=-1 Vậy x=-1

hoaiphuong85 · Answer

(2x - 1)^4 = 81 => (2x - 1)^4 = 3^4 => 2x - 1 = (+-3) => ( left[ begin{array}{l}2x - 1 = -3 2x - 1 = 3 end{array} right. ) => ( left[ begin{array}{l}2x = (-3) + 1 2x = 3 + 1 end{array} right. ) => ( left[ begin{array}{l}2x = -2 2x = 4 end{array} right. ) => ( left[ begin{array}{l}x=-1 x=2 end{array} right. ) Vậy x in {-1; 2} 5^x + 5^{x + 2} = 650 <=> 5^x . 1 + 5^x . 5^2 = 650 <=> 5^x(1 + 5^2) = 650 <=> 5^x(1 + 25) = 650 <=> 5^x . 26 = 650 <=> 5^x = 650 : 26 <=> 5^x = 25 <=> 5^x = 5^2 <=> x = 2 Vậy x = 2 (x - 1)^5 = -32 => (x - 1)^5 = (-2)^5 => x - 1 = -2 => x = (-2) + 1 => x = -1 Vậy x = -1