Issolvi M=(2x-1)^2-(x+3)^2

$$M = ( 2 x - 1 ) ^ { 2 } - ( x + 3 ) ^ { 2 }$$

Solvi għal M

$$M=\left(x-4\right)\left(3x+2\right)$$

Passi tas-Soluzzjonijiet

Uża teorema binomjali \left(a-b\right)^{2}=a^{2}-2ab+b^{2} biex tespandi \left(2x-1\right)^{2}.

$$M=4x^{2}-4x+1-\left(x+3\right)^{2}$$

Uża teorema binomjali \left(a+b\right)^{2}=a^{2}+2ab+b^{2} biex tespandi \left(x+3\right)^{2}.

$$M=4x^{2}-4x+1-\left(x^{2}+6x+9\right)$$

Biex issib l-oppost ta' x^{2}+6x+9, sib l-oppost ta' kull terminu.

$$M=4x^{2}-4x+1-x^{2}-6x-9$$

Ikkombina 4x^{2} u -x^{2} biex tikseb 3x^{2}.

$$M=3x^{2}-4x+1-6x-9$$

Ikkombina -4x u -6x biex tikseb -10x.

$$M=3x^{2}-10x+1-9$$

Naqqas 9 minn 1 biex tikseb -8.

$$M=3x^{2}-10x-8$$

Solvi għal x (complex solution)

$$x=\frac{-\sqrt{3M+49}+5}{3}$$

$$x=\frac{\sqrt{3M+49}+5}{3}$$

Solvi għal x

$$x=\frac{-\sqrt{3M+49}+5}{3}$$

$$x=\frac{\sqrt{3M+49}+5}{3}\text{, }M\geq -\frac{49}{3}$$