Question

Solve
(x-1)2(x+3)2 = 26
​

Answer 1

Answer:

Given equation is,

      (x - 1)2(x + 3)2 = 26

      (x - 1) (x +3) = $\frac{26}{4}$

      x² + 3x - x - 3 = $\frac{13}{2}$

     (x² + 2x  - 3)2 = 13

     2x² + 4x - 6 = 13

     2x² + 4x -6 -13 = 0

     2x² + 4x - 19 = 0

We know the formula,

                  $x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

Here, a = 2

         b = 4

         c = -19

∴ $x=\frac{-4\pm \sqrt{4^2-4\cdot \:2\left(-19\right)}}{2\cdot \:2}$

 $x=\frac{-4\pm \:2\sqrt{42}}{2\cdot \:2}$

 $x=\frac{-4+2\sqrt{42}}{2\cdot \:2}, \:x=\frac{-4-2\sqrt{42}}{2\cdot \:2}$

 $x=\frac{-2+\sqrt{42}}{2}, \:x=-\frac{2+\sqrt{42}}{2}$

                       Hope it helps you^_^