Question

Tìm x biết:

a) \(2\left(x+2\right)^2-100=62\)

b) \(5.2^x-2^{x+1}=48\)

Answer 1

a)  2(x + 2)² - 100 = 62

=> 2(x + 2)² = 62 + 100

=> 2(x + 2)² = 162

=> (x + 2)²  = 162 : 2

=> (x + 2)²  = 81

mà \(9^2=81\) và \(\left(-9\right)^2=81\)

nên x + 2 = 9    và x + 2 = -9

* x  + 2 = 9           => x = 9 - 2 = 7

* x + 2 = -9           => x = -9 - 2 = -11 

b) 5 . 2^x - 2^{x  + 1} =  48

=>  5 . 2^x - 2^x  . 2 = 48

=> 2^x (5 - 2) = 48

=> 2^x . 3 = 48

=> 2^x = 48  : 3

=> 2^x = 16

=> x = 4 

Answer 2

\(a)2(x+2)^2-100\)\(=62\)

suy ra \(2(x+2)^2 =62+100\)

suy ra \(2(x+2)^2=162\)

suy ra \((x+2)^2=162/2\)

suy ra \((x+2)^2=81\)

suy ra\(x+2=9 hay x+2=-9\)

suy ra x=9-2=7 hay x=-9-2=-11

b)5.2^x-2^x+1=48

suy ra \(5.2^x-2^x.2=48\)

 

suy ra \(2^x.(5-2)=48\)

suy ra \(2^x.3=48\)

suy ra \(2^x=48/3=16\)

suy ra\(2^x=2^4\)

suy ra \(x=4\)