Issolvi 2x^2-4x+3=2(x-p)^2+q

$$2 x ^ { 2 } - 4 x + 3 = 2 ( x - p ) ^ { 2 } + q$$

Solvi għal q

$$q=4px-4x-2p^{2}+3$$

Passi tas-Soluzzjonijiet

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

$$2x^{2}-4x+3=2\left(x^{2}-2xp+p^{2}\right)+q$$

Uża l-propjetà distributtiva biex timmultiplika 2 b'x^{2}-2xp+p^{2}.

$$2x^{2}-4x+3=2x^{2}-4xp+2p^{2}+q$$

Ibdel in-naħat sabiex it-termini varjabbli kollha jkunu fuq in-naħa tax-xellug.

$$2x^{2}-4xp+2p^{2}+q=2x^{2}-4x+3$$

Naqqas 2x^{2} miż-żewġ naħat.

$$-4xp+2p^{2}+q=2x^{2}-4x+3-2x^{2}$$

Ikkombina 2x^{2} u -2x^{2} biex tikseb 0.

$$-4xp+2p^{2}+q=-4x+3$$

Żid 4xp maż-żewġ naħat.

$$2p^{2}+q=-4x+3+4xp$$

Naqqas 2p^{2} miż-żewġ naħat.

$$q=-4x+3+4xp-2p^{2}$$

Solvi għal p (complex solution)

$$p=\frac{\sqrt{4x^{2}-8x-2q+6}}{2}+x$$

$$p=-\frac{\sqrt{4x^{2}-8x-2q+6}}{2}+x$$

Solvi għal p

$$p=\frac{\sqrt{4x^{2}-8x-2q+6}}{2}+x$$

$$p=-\frac{\sqrt{4x^{2}-8x-2q+6}}{2}+x\text{, }q\leq 2x^{2}-4x+3$$