Question

Tìm x, biết:

I x-2 I = x

\(\left(2x-3\right)^2=9\)

\(x^2+1=82\)

\(x^2+\frac{7}{4}=\frac{23}{4}\)

\(\left(2x+3\right)^2=25\)

Answer 1

|x-2|=x

+) x-2=x

=> x-x=2

=> 0=2 (vô lí, loại)

+) x-2=-x

=> x+x=2

=> 2x=2

=> x=1

Vậy x=1.

(2x-3)²=9

=> (2x-3)²=3²=(-3)²

+) 2x-3=3

=> 2x=3+3

=> 2x=6

=> x=3

+) 2x-3=-3

=> 2x=-3+3

=> 2x=0

=> x=0

Vạy x \(\in\){0; 3}.

x²+1=82

=> x²=82-1

=> x²=81

=> x²=9²=(-9)²

Vậy \(x\in\left\{-9;9\right\}\).

x²+7/4 = 23/4

=> x²=23/4 - 7/4

=> x²=16/4

=> x²=4

=> x²=2²=(-2)²

Vậy \(x\in\left\{-2;2\right\}\).

(2x+3)²=25

=> (2x+3)²=5²=(-5)²

+) 2x+3=5

=> 2x=5-3

=> 2x=2

=> x=1

+) 2x+3=-5

=> 2x=-5-3

=> 2x=-8

=> x=-4

Vậy x \(\in\){-4;1}.