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CBSE Class 10 Answered

Solve for x in the equation 2m(1+x²)-(1+m²)(x+m)=0
Asked by vikasg13.hardware | 07 Aug, 2018, 04:52: PM
answered-by-expert Expert Answer
2m (1 + x²) - (1 + m²)(x + m) = 0
2m + 2mx2 - (x + m + m2 x + m3) = 0
2m + 2mx2 - x - m - m2 x - m3 = 0
2mx2 - (1 + m2)x + m - m3 = 0
begin mathsize 16px style straight x space equals space fraction numerator left parenthesis 1 space plus space straight m squared right parenthesis plus-or-minus square root of left parenthesis 1 space plus space straight m squared right parenthesis squared minus 4 cross times 2 straight m cross times left parenthesis straight m space minus space straight m cubed right parenthesis end root over denominator 4 straight m end fraction
Consider comma
left parenthesis 1 space plus space straight m squared right parenthesis squared minus 4 cross times 2 straight m cross times left parenthesis straight m space minus space straight m cubed right parenthesis
equals 1 plus 2 straight m squared plus straight m to the power of 4 minus 8 straight m left parenthesis straight m space minus space straight m cubed right parenthesis
equals 1 plus 2 straight m squared plus straight m to the power of 4 minus 8 straight m squared plus 8 straight m to the power of 4
equals 9 straight m to the power of 4 minus 6 straight m squared plus 1
equals left parenthesis 3 straight m squared minus 1 right parenthesis squared
rightwards double arrow square root of left parenthesis 1 space plus space straight m squared right parenthesis squared minus 4 cross times 2 straight m cross times left parenthesis straight m space minus space straight m cubed right parenthesis end root equals 3 straight m squared minus 1
straight x equals fraction numerator left parenthesis 1 space plus space straight m squared right parenthesis plus-or-minus open parentheses 3 straight m squared minus 1 close parentheses over denominator 4 straight m end fraction
straight x equals fraction numerator left parenthesis 1 space plus space straight m squared right parenthesis plus open parentheses 3 straight m squared minus 1 close parentheses over denominator 4 straight m end fraction space or space fraction numerator left parenthesis 1 space plus space straight m squared right parenthesis minus open parentheses 3 straight m squared minus 1 close parentheses over denominator 4 straight m end fraction
straight x equals fraction numerator 4 straight m squared over denominator 4 straight m end fraction space or space fraction numerator 2 minus 2 straight m squared over denominator 4 straight m end fraction
straight x equals straight m space or space fraction numerator 1 minus straight m squared over denominator 2 straight m end fraction end style
Answered by Sneha shidid | 08 Aug, 2018, 09:41: AM

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