☺ Salut ☺
[tex]\rule{6cm}{1mm}[/tex]
[tex]A = 169{x}^{2} - 121 - (13x - 11)(9x + 4)[/tex]
[tex]D\acute{e}veloppons\;et\;r\acute{e}duisons\;{l}^{,}expression\;A\;:[/tex]
[tex]A = 169{x}^{2} - 121 - (13x - 11)(9x + 4)[/tex]
[tex]A = 169{x}^{2} - 121 - 117{x}^{2} - 52x + 99x + 44[/tex]
[tex]\boxed{\boxed{\green{A = 52{x}^{2} + 47x - 77}}}[/tex]
[tex]\\[/tex]
[tex]Factorisons\;{l}^{,}expression\;169{x}^{2} - 121\;:[/tex]
[tex]169{x}^{2} - 121[/tex]
[tex]On\; sait\;que\;{a}^{2} - {b}^{2} = (a - b)(a + b)[/tex]
[tex]Alors\;:[/tex]
[tex]\boxed{\boxed{\green{(13x - 11)(13x + 11)}}}[/tex]
[tex]\\[/tex]
[tex]Factorisons\;A\;:[/tex]
[tex]A = 169{x}^{2} - 121 - (13x - 11)(9x + 4)[/tex]
[tex]A = (13x - 11)(13x + 11) - (13x - 11)(9x + 4)[/tex]
[tex]A = (13x - 11) [(13x + 11) - (9x + 4)][/tex]
[tex]A = (13x - 11)(13x + 11 - 9x - 4)[/tex]
[tex]\boxed{\boxed{\green{A = (13x - 11)(4x + 7)}}}[/tex]
[tex]\\[/tex]
[tex] Donnons\;les\; solution\;de\;{l}^{,}\acute{e}quation\;A = 0\;:[/tex]
[tex]A = (13x - 11)(4x + 7)[/tex]
[tex](13x - 11)(4x + 7) = 0[/tex]
[tex]On\;a\;:[/tex]
[tex]13x - 11 = 0 \;et\;4x + 7 = 0[/tex]
[tex]13x = 11 \;et\;4x = - 7[/tex]
[tex]x = \dfrac{11}{13} \;et\;x = - \dfrac{7}{4}[/tex]
[tex]\boxed{\boxed{\green{S = \{- \dfrac{7}{4} ; \dfrac{11}{13} \}}}}[/tex]
[tex]\rule{6cm}{1mm}[/tex]
