Toán Lớp 9: Bài 1 : Giải các phương trình sau :
√x -2 = 0
5 -2√(x-1) = 3
√(x^2+1) = x-1
√(x^2+2x+1)=5
√(〖4x〗^2-4x+1)= x-1
3√(x+1) + 1/2 √(x+1) = 7
√(4x-12) + √(9x-27)-4√(x-3) + 3x – 3= 0
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Toán Lớp 9: Bài 1 : Giải các phương trình sau :
√x -2 = 0
5 -2√(x-1) = 3
√(x^2+1) = x-1
√(x^2+2x+1)=5
√(〖4x〗^2-4x+1)= x-1
3√(x+1) + 1/2 √(x+1) = 7
√(4x-12) + √(9x-27)-4√(x-3) + 3x – 3= 0
Comments ( 1 )
$⇔$ 2$\sqrt{x-1}$ $=2$
$⇔$ $\sqrt{x-1}$ $= 1$
$⇔ x-1=1 ⇔ x=2$
c) $\sqrt{x²+1}$ $= x-1$
$⇔ x²+1 = (x-1)²=x²-2x+1$
$⇔ 2x=0 ⇔ x=0(KTM)$
$d)$ $\sqrt{x²+2x+1}$ $=5$
$⇔$ $\sqrt{(x+1)²}$ $=5$
$⇔ |x+1|=5 $
Với $x≥-1$ thì $x+1=5 ⇔ x=4(T/m)$
Với $x<-1$ thì $-x-1=5$
$⇔ x=-6(T/m)$