9x^2-3(a^2+b^2)x+a^2b^2=0 Using quadratic formula solve for x.

1.	9x^2-3(a^2+b^2)x+a^2b^2=0 Using quadratic formula solve for x.
Answer» D = b2 - 4ac{tex}= ( - 9 ( a + b ) ) ^ { 2 } - 4 \\times 9 \\times \\left( 2 a ^ { 2 } + 5 a b + 2 a b ^ { 2 } \\right){/tex}= 81(a + b)2 - 36(2a2 + 5ab + 2b2)= 9[9(a2 + b2 + 2ab - 8a2 - 20ab - 8b2)]= 9[a2 + b2 - 2ab]= 9(a - b)2{tex}x = \\frac { - b \\pm \\sqrt { D } } { 2 a } = \\frac { 9 ( a + b ) \\pm \\sqrt { 9 ( a - b ) ^ { 2 } } } { 2 \\times 9 }{/tex}{tex}{ \\Rightarrow x = 3 \\frac { [ 3 ( a + b ) \\pm ( a - b ) ] } { 2 \\times 9 } }{/tex}{tex}{ \\Rightarrow x = \\frac { ( 3 a + 3 b ) \\pm ( a - b ) } { 6 } }{/tex}{tex}\\Rightarrow x = \\frac { 3 a + 3 b + a - b } { 6 } \\text { or } x = \\frac { 3 a + 3 b - a + b } { 6 }{/tex}{tex}\\Rightarrow x = \\frac { 4 a + 2 b } { 6 } \\text { or } x = \\frac { 2 a + 4 b } { 6 }{/tex}{tex}\\Rightarrow x = \\frac { 2 a + b } { 3 } \\text { or } x = \\frac { a + 2 b } { 3 }{/tex}

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