Factorise (9X-1/5)2 + (X+1/3)2

Dear student We have,9x-152+x+132=81x2+125-185x+x2+19+23x=82x2-44x15+34225=22259225x2-330x+17Now we will solve the quadratic equation 9225x2-330x+17 by discriminant method, we getx=--330±3302-492251729225x=330±108900-62730018450x=330±-51840018450x=330±720i18450x=33018450±720i18450x=11615±8i205So, 9x-152+x+132=2225x-11615+8i205x-11615-8i205 Regards

Factorise (9X-1/5)²+ (X+1/3)²

Dear student

W e h a v e, {(9 x - \frac{1}{5})}^{2} + {(x + \frac{1}{3})}^{2} = (81 x^{2} + \frac{1}{25} - \frac{18}{5} x) + (x^{2} + \frac{1}{9} + \frac{2}{3} x) = 82 x^{2} - \frac{44 x}{15} + \frac{34}{225} = \frac{2}{225} (9225 x^{2} - 330 x + 17) N o w w e w i l l s o l v e t h e q u a d r a t i c e q u a t i o n 9225 x^{2} - 330 x + 17 b y d i s c r i m i n a n t m e t h o d, w e g e t x = \frac{- (- 330) \pm \sqrt{{(330)}^{2} - 4 (9225) (17)}}{2 (9225)} x = \frac{330 \pm \sqrt{108900 - 627300}}{18450} x = \frac{330 \pm \sqrt{- 518400}}{18450} x = \frac{330 \pm 720 i}{18450} x = \frac{330}{18450} \pm \frac{720 i}{18450} x = \frac{11}{615} \pm \frac{8 i}{205} S o, {(9 x - \frac{1}{5})}^{2} + {(x + \frac{1}{3})}^{2} = \frac{2}{225} [x - (\frac{11}{615} + \frac{8 i}{205})] [x - (\frac{11}{615} - \frac{8 i}{205})]

Regards

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