Question

Tìm x biết:

a) ( x-2)³ = 27

b) 2^x + 2^x+3= 144

c) ( 2x-3)²= 25

d) ( 2x-1)¹⁰= ( 2x-1) ¹⁰⁰

Answer 1

a. (x-2)³=27

<=> (x-2)³=3³

=> x-2=3 =>x=5

c.(2x-3)²=25

<=> (2x-3)²=5²

=>2x-3=5 => 2x=8 =>x=4

Answer 2

a) ( x-2)³ = 27

(x-2)3 = 3³

x-2 = 3

x = 5

b) 2^x + 2^x+3= 144

2^x ( 1 + 2³ ) = 144

2^x . 9 = 144

2^x = 16

2^x = 2⁴

x = 4

c) ( 2x-3)²= 25

(2x-3)² = 5²

2x-3 = 5

2x = 8

x = 4

d) ( 2x-1)¹⁰= ( 2x-1) ¹⁰⁰

Dễ thấy 2x - 1 = 0 vì 0¹⁰ = 0¹⁰⁰

Vậy x = 0,5

Nếu 2x - 1 \(\ne\)0 

( 2x - 1 )¹⁰ : ( 2x - 1 )¹⁰ = ( 2x - 1 )¹⁰⁰ : ( 2x - 1 )¹⁰

( 2x - 1 )⁹⁰ = 1

Vậy 2x - 1 = 1 hoặc - 1.

Vậy x = 1 ; 0 ; 0,5.