Issolvi 1/(x-1)^2=y

$$\frac { 1 } { ( x - 1 ) ^ { 2 } } = y$$

Solvi għal y

$$y=\frac{1}{\left(x-1\right)^{2}}$$

$$x\neq 1$$

Passi biex Issolvi l-Ekwazzjoni Lineari

Immultiplika ż-żewġ naħat tal-ekwazzjoni b'\left(x-1\right)^{2}.

$$1=y\left(x-1\right)^{2}$$

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

$$1=y\left(x^{2}-2x+1\right)$$

Uża l-propjetà distributtiva biex timmultiplika y b'x^{2}-2x+1.

$$1=yx^{2}-2yx+y$$

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

$$yx^{2}-2yx+y=1$$

Ikkombina t-termini kollha li fihom y.

$$\left(x^{2}-2x+1\right)y=1$$

Iddividi ż-żewġ naħat b'x^{2}-2x+1.

$$\frac{\left(x^{2}-2x+1\right)y}{x^{2}-2x+1}=\frac{1}{x^{2}-2x+1}$$

Meta tiddividi b'x^{2}-2x+1 titneħħa l-multiplikazzjoni b'x^{2}-2x+1.

$$y=\frac{1}{x^{2}-2x+1}$$

Iddividi 1 b'x^{2}-2x+1.

$$y=\frac{1}{\left(x-1\right)^{2}}$$

Solvi għal x (complex solution)

$$x=1-y^{-\frac{1}{2}}$$

$$x=y^{-\frac{1}{2}}+1\text{, }y\neq 0$$

Solvi għal x

$$x=1+\frac{1}{\sqrt{y}}$$

$$x=1-\frac{1}{\sqrt{y}}\text{, }y>0$$