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Solve quadratic equation for x 4x² - 4a²x + ( a⁴ - b⁴ ) =0 |
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Answer» 4x2-4a2x+(a4-b4)=0a = 4, b = -4a{tex}^2{/tex}, c =\xa0{tex}a^4-b^4{/tex}D =\xa0{tex}b^{2}-4 a c{/tex}=\xa0{tex}\\left(-4 a^{2}\\right)^{2}-4 \\times 4 \\times\\left(a^{4}-b^{4}\\right){/tex}{tex}=16 a^{4}-16 a^{4}+16 b^{4}{/tex}D = 16 b4Therefore,by quadratic formula,we have,{tex}x=\\frac{-b \\pm \\sqrt{D} }{ 2 a}{/tex}{tex}=\\frac{-\\left(-4 a^{2}\\right) \\pm 4 b^{2}}{2 \\times 4}{/tex}{tex}=\\frac{4 a^{2} \\pm 4 b^{2}} {8}{/tex}x =\xa0{tex}\\frac{ a^{2}\\pm b^2} {2}{/tex}x =\xa0{tex}\\frac{a^2+b^2}{2}{/tex} or x={tex}\\frac{a^2-b^2}{2}{/tex}\xa0\xa0{tex}{/tex}\xa0{tex}{/tex}Hence,the roots of given quadratic equation is ,{tex}\\frac{a^2+b^2}{2} ,\\frac{a^2-b^2}{2}{/tex} yeah you are right |
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